Bulletin des Sciences Mathematiques最新文献

{"title":"Invariant p-complements normalized by the fixed point subgroup","authors":"Hangyang Meng ,&nbsp;Xingyu Zhang","doi":"10.1016/j.bulsci.2025.103635","DOIUrl":"10.1016/j.bulsci.2025.103635","url":null,"abstract":"<div><div>Let a group <em>A</em> act on a group <em>G</em> coprimely, i.e., <span><math><mo>(</mo><mo>|</mo><mi>A</mi><mo>|</mo><mo>,</mo><mo>|</mo><mi>G</mi><mo>|</mo><mo>)</mo><mo>=</mo><mn>1</mn></math></span>. We say that <em>G</em> is <em>A</em>-<em>p</em>-nilpotent if <em>G</em> has an <em>A</em>-invariant <span><math><mi>Hall</mi><mspace></mspace><msup><mrow><mi>p</mi></mrow><mrow><mo>′</mo></mrow></msup></math></span>-subgroup normalized by <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>(</mo><mi>A</mi><mo>)</mo></math></span>. In this paper, we give some equivalent descriptions on <em>A</em>-<em>p</em>-nilpotence by analyzing the structure of minimal non-<em>A</em>-<em>p</em>-nilpotent groups. This is a follow-up work to A. Beltrán's research.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"202 ","pages":"Article 103635"},"PeriodicalIF":1.3,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143807280","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Global existence of strong solutions to the 3D incompressible magnetohydrodynamics equations with zero heat-conduction","authors":"Jinxia Liang ,&nbsp;Xinqiu Zhang","doi":"10.1016/j.bulsci.2025.103625","DOIUrl":"10.1016/j.bulsci.2025.103625","url":null,"abstract":"<div><div>In this paper, we study an initial-boundary value problem of three-dimensional inhomogeneous incompressible magnetohydrodynamics (MHD) fluids with vacuum, zero heat-conduction and density-temperature-dependent viscosity and magnetic diffusive coefficients. Based on the time-weighted a priori estimates, we establish the global existence and exponential decay properties of strong solutions under the conditions that the initial energy is suitably small.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"202 ","pages":"Article 103625"},"PeriodicalIF":1.3,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143785262","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Perturbations of a system of general functional equations in several variables","authors":"Hamid Khodaei","doi":"10.1016/j.bulsci.2025.103624","DOIUrl":"10.1016/j.bulsci.2025.103624","url":null,"abstract":"<div><div>Pólya and Szegő <span><span>[53, Teil I, Aufgabe 99]</span></span> proved that every approximate sequence of reals is near an additive sequence. Bourgin <span><span>[11]</span></span> showed that every approximate ring homomorphism from a Banach algebra onto a unital Banach algebra is necessarily a ring homomorphism. We deal with Pólya-Szegő's result for a general functional equation and a system of general functional equations in several variables. To do this, we shall use a different direct method from the previous studies. In consequence, Bourgin's result for approximate homomorphisms and Lie homomorphisms on Banach algebras are discussed. Several examples for comparison with previous studies are included.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"202 ","pages":"Article 103624"},"PeriodicalIF":1.3,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143768977","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Subnormal transcendental meromorphic solutions of delay differential equations","authors":"Mengting Xia,&nbsp;Jianren Long,&nbsp;Xuxu Xiang","doi":"10.1016/j.bulsci.2025.103623","DOIUrl":"10.1016/j.bulsci.2025.103623","url":null,"abstract":"<div><div>The following two delay differential equations are studied,<span><span><span><math><mi>ω</mi><msup><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow><mrow><mi>k</mi></mrow></msup><munderover><mo>∑</mo><mrow><mi>μ</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>s</mi></mrow></munderover><msub><mrow><mi>e</mi></mrow><mrow><mi>μ</mi></mrow></msub><mo>(</mo><mi>z</mi><mo>)</mo><mi>ω</mi><mo>(</mo><mi>z</mi><mo>+</mo><msub><mrow><mi>c</mi></mrow><mrow><mi>μ</mi></mrow></msub><mo>)</mo><mo>+</mo><mi>a</mi><mo>(</mo><mi>z</mi><mo>)</mo><mfrac><mrow><msup><mrow><mi>ω</mi></mrow><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow></msup><mo>(</mo><mi>z</mi><mo>)</mo></mrow><mrow><mi>ω</mi><mo>(</mo><mi>z</mi><mo>)</mo></mrow></mfrac><mo>=</mo><mi>R</mi><mo>(</mo><mi>z</mi><mo>,</mo><mi>ω</mi><mo>(</mo><mi>z</mi><mo>)</mo><mo>)</mo><mo>,</mo></math></span></span></span> and<span><span><span><math><mo>(</mo><mi>ω</mi><mo>(</mo><mi>z</mi><mo>)</mo><mi>ω</mi><mo>(</mo><mi>z</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>−</mo><mn>1</mn><mo>)</mo><mo>(</mo><mi>ω</mi><mo>(</mo><mi>z</mi><mo>)</mo><mi>ω</mi><mo>(</mo><mi>z</mi><mo>−</mo><mn>1</mn><mo>)</mo><mo>−</mo><mn>1</mn><mo>)</mo><mo>+</mo><mi>a</mi><mo>(</mo><mi>z</mi><mo>)</mo><mfrac><mrow><msup><mrow><mi>ω</mi></mrow><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow></msup><mo>(</mo><mi>z</mi><mo>)</mo></mrow><mrow><mi>ω</mi><mo>(</mo><mi>z</mi><mo>)</mo></mrow></mfrac><mo>=</mo><mi>R</mi><mo>(</mo><mi>z</mi><mo>,</mo><mi>ω</mi><mo>(</mo><mi>z</mi><mo>)</mo><mo>)</mo><mo>,</mo></math></span></span></span></div><div>where <span><math><mi>k</mi><mo>≥</mo><mn>0</mn></math></span>, <span><math><mi>n</mi><mo>≥</mo><mn>1</mn></math></span>, <span><math><mi>s</mi><mo>≥</mo><mn>1</mn></math></span> are integers, <span><math><msub><mrow><mi>c</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>, <span><math><mo>.</mo><mo>.</mo><mo>.</mo></math></span>, <span><math><msub><mrow><mi>c</mi></mrow><mrow><mi>s</mi></mrow></msub></math></span> are nonzero complex numbers, <span><math><mi>a</mi><mo>(</mo><mi>z</mi><mo>)</mo></math></span>, <span><math><msub><mrow><mi>e</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mi>z</mi><mo>)</mo></math></span>, <span><math><mo>.</mo><mo>.</mo><mo>.</mo></math></span>, <span><math><msub><mrow><mi>e</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>(</mo><mi>z</mi><mo>)</mo></math></span> are small with respect to <em>ω</em>, <span><math><mi>R</mi><mo>(</mo><mi>z</mi><mo>,</mo><mi>ω</mi><mo>)</mo></math></span> is rational in <em>ω</em> with small meromorphic coefficients with respect to <em>ω</em>. The necessary conditions for the existence of subnormal transcendental meromorphic solutions of the above two equations are obtained, which extend the previous results from Cao, Chen and Korhonen <span><span>[2]</span></span>, Halburd and Korhonen <span><span>[6]</span></span>, Korhonen and Liu <span><span>[12]</span></span>. Some examples are given to support these results.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"202 ","pages":"Article 103623"},"PeriodicalIF":1.3,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143785348","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Weighted Cesàro type operators between weighted Bergman spaces","authors":"Petros Galanopoulos ,&nbsp;Aristomenis G. Siskakis ,&nbsp;Ruhan Zhao","doi":"10.1016/j.bulsci.2025.103622","DOIUrl":"10.1016/j.bulsci.2025.103622","url":null,"abstract":"<div><div>Let <span><math><mi>D</mi></math></span> be the open unit disk in the complex plane <span><math><mi>C</mi></math></span>. Let <em>μ</em> be a positive Borel measure on <span><math><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span>. If <span><math><mi>f</mi><mo>(</mo><mi>z</mi><mo>)</mo><mo>=</mo><msubsup><mrow><mo>∑</mo></mrow><mrow><mi>n</mi><mo>=</mo><mn>0</mn></mrow><mrow><mo>∞</mo></mrow></msubsup><msub><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msub><msup><mrow><mi>z</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> is an analytic function in <span><math><mi>D</mi></math></span>, we consider for <span><math><mi>β</mi><mo>&gt;</mo><mn>0</mn></math></span> the following weighted Cesàro type operator<span><span><span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>μ</mi><mo>,</mo><mi>β</mi></mrow></msub><mo>(</mo><mi>f</mi><mo>)</mo><mo>(</mo><mi>z</mi><mo>)</mo><mo>=</mo><munderover><mo>∑</mo><mrow><mi>n</mi><mo>=</mo><mn>0</mn></mrow><mrow><mo>∞</mo></mrow></munderover><msub><mrow><mi>μ</mi></mrow><mrow><mi>n</mi></mrow></msub><mrow><mo>(</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>n</mi></mrow></munderover><mfrac><mrow><mi>Γ</mi><mo>(</mo><mi>n</mi><mo>−</mo><mi>k</mi><mo>+</mo><mi>β</mi><mo>)</mo></mrow><mrow><mo>(</mo><mi>n</mi><mo>−</mo><mi>k</mi><mo>)</mo><mo>!</mo><mspace></mspace><mi>Γ</mi><mo>(</mo><mi>β</mi><mo>)</mo></mrow></mfrac><msub><mrow><mi>a</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>)</mo></mrow><msup><mrow><mi>z</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>,</mo><mspace></mspace><mi>z</mi><mo>∈</mo><mi>D</mi><mo>,</mo></math></span></span></span> where <span><math><msub><mrow><mi>μ</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> is the <em>n</em>-th moment of <em>μ</em> given by <span><math><msub><mrow><mi>μ</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>=</mo><munder><mo>∫</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></munder><msup><mrow><mi>t</mi></mrow><mrow><mi>n</mi></mrow></msup><mspace></mspace><mi>d</mi><mi>μ</mi><mo>(</mo><mi>t</mi><mo>)</mo></math></span>. We characterize boundedness of the weighted Cesàro type operator <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>μ</mi><mo>,</mo><mi>β</mi></mrow></msub></math></span> from the weighted Bergman space <span><math><msubsup><mrow><mi>A</mi></mrow><mrow><mi>α</mi></mrow><mrow><mi>p</mi></mrow></msubsup></math></span> to <span><math><msubsup><mrow><mi>A</mi></mrow><mrow><mi>α</mi></mrow><mrow><mi>q</mi></mrow></msubsup></math></span> for <span><math><mn>1</mn><mo>≤</mo><mi>p</mi><mo>≤</mo><mi>q</mi><mo>&lt;</mo><mo>∞</mo></math></span>. Our method relies on a representation of <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>μ</mi><mo>,</mo><mi>β</mi></mrow></msub></math></span> as an integral operator with a kernel and a generalized Schur's test.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"202 ","pages":"Article 103622"},"PeriodicalIF":1.3,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143785261","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On character variety of Anosov representations","authors":"Krishnendu Gongopadhyay,&nbsp;Tathagata Nayak","doi":"10.1016/j.bulsci.2025.103621","DOIUrl":"10.1016/j.bulsci.2025.103621","url":null,"abstract":"<div><div>Let Γ be the fundamental group of a <em>k</em>-punctured, <span><math><mi>k</mi><mo>≥</mo><mn>0</mn></math></span>, closed connected orientable surface of genus <span><math><mi>g</mi><mo>≥</mo><mn>2</mn></math></span>. We show that the character variety of the <span><math><mo>(</mo><msup><mrow><mi>Q</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>,</mo><msup><mrow><mi>Q</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>)</mo></math></span>-Anosov irreducible representations, resp. the character variety of the <span><math><mo>(</mo><msup><mrow><mi>P</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>,</mo><msup><mrow><mi>P</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>)</mo></math></span>-Anosov Zariski dense representations of Γ into <span><math><mrow><mi>SL</mi></mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></span>, <span><math><mi>n</mi><mo>≥</mo><mn>2</mn></math></span>, is a complex manifold of complex dimension <span><math><mo>(</mo><mn>2</mn><mi>g</mi><mo>+</mo><mi>k</mi><mo>−</mo><mn>2</mn><mo>)</mo><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>−</mo><mn>1</mn><mo>)</mo></math></span>. For <span><math><mi>Γ</mi><mo>=</mo><msub><mrow><mi>π</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><msub><mrow><mi>Σ</mi></mrow><mrow><mi>g</mi></mrow></msub><mo>)</mo></math></span>, we also show that these character varieties are holomorphic symplectic manifolds.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"202 ","pages":"Article 103621"},"PeriodicalIF":1.3,"publicationDate":"2025-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143760968","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A q-congruence implying the Beukers–Van Hamme congruence","authors":"Victor J.W. Guo ,&nbsp;Ji-Cai Liu","doi":"10.1016/j.bulsci.2025.103615","DOIUrl":"10.1016/j.bulsci.2025.103615","url":null,"abstract":"&lt;div&gt;&lt;div&gt;By making use of Andrews' terminating &lt;em&gt;q&lt;/em&gt;-analogue of Watson's formula and a double sum identity, we give a &lt;em&gt;q&lt;/em&gt;-analogue of the following congruence: for any prime &lt;span&gt;&lt;math&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;≡&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;mod&lt;/mi&gt;&lt;/mrow&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;,&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;munderover&gt;&lt;mo&gt;∑&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/munderover&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mo&gt;≡&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/mrow&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;mod&lt;/mi&gt;&lt;/mrow&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; In view of the Chowla–Dwork–Evans congruence, our &lt;em&gt;q&lt;/em&gt;-congruence may somewhat be regarded as a &lt;em&gt;q&lt;/em&gt;-analogue of the Beukers–Van Hamme congruence:&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;munderover&gt;&lt;mo&gt;∑&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/munderover&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mo&gt;≡&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;mod&lt;/mi&gt;&lt;/mrow&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; where &lt;span&gt;&lt;math&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; with &lt;span&gt;&lt;math&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"201 ","pages":"Article 103615"},"PeriodicalIF":1.3,"publicationDate":"2025-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143682036","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On global well-posedness, scattering and other properties for infinity energy solutions to the inhomogeneous NLS equation","authors":"Roger P. de Moura,&nbsp;Mykael Cardoso,&nbsp;Gleison N. Santos","doi":"10.1016/j.bulsci.2025.103620","DOIUrl":"10.1016/j.bulsci.2025.103620","url":null,"abstract":"<div><div>In this work, we consider the inhomogeneous nonlinear Schrödinger (INLS) equation in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span><span><span><span><math><mrow><mi>i</mi><msub><mrow><mo>∂</mo></mrow><mrow><mi>t</mi></mrow></msub><mi>u</mi><mo>+</mo><mi>Δ</mi><mi>u</mi><mo>+</mo><mi>γ</mi><mo>|</mo><mi>x</mi><msup><mrow><mo>|</mo></mrow><mrow><mo>−</mo><mi>b</mi></mrow></msup><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>α</mi></mrow></msup><mi>u</mi><mo>=</mo><mn>0</mn><mo>,</mo></mrow></math></span></span></span> where <span><math><mi>γ</mi><mo>=</mo><mo>±</mo><mn>1</mn></math></span>, and <em>α</em> and <em>b</em> are positive numbers. Our main focus is to establish the global well-posedness of the INLS equation in Lorentz spaces for <span><math><mn>0</mn><mo>&lt;</mo><mi>b</mi><mo>&lt;</mo><mn>2</mn></math></span> and <span><math><mi>α</mi><mo>&lt;</mo><mfrac><mrow><mn>4</mn><mo>−</mo><mn>2</mn><mi>b</mi></mrow><mrow><mi>N</mi><mo>−</mo><mn>2</mn></mrow></mfrac></math></span>. To achieve this, we use Strichartz estimates in Lorentz spaces <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>r</mi><mo>,</mo><mi>q</mi></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></math></span> combined with a fixed point argument. Working on Lorentz space setting instead the classical <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> is motivated by the fact that the potential <span><math><mo>|</mo><mi>x</mi><msup><mrow><mo>|</mo></mrow><mrow><mo>−</mo><mi>b</mi></mrow></msup></math></span> does not belong the usual <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>-space. As a consequence of the ideas developed here on the global solution study we obtain some other properties for INLS, such as, existence of self-similar solutions, scattering, wave operators and asymptotic stability.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"201 ","pages":"Article 103620"},"PeriodicalIF":1.3,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143697012","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Some new Lucas sequence versions of Wolstenholme's congruence","authors":"Yanteng Lu ,&nbsp;Peng Yang ,&nbsp;Tianxin Cai","doi":"10.1016/j.bulsci.2025.103619","DOIUrl":"10.1016/j.bulsci.2025.103619","url":null,"abstract":"<div><div>In this paper, we extend the results of He, Mao, and Togbé, as well as Yang and Yang, and give some Lucas sequence versions generalizations of Wolstenholme's theorem with multiple harmonic sums.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"202 ","pages":"Article 103619"},"PeriodicalIF":1.3,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143686003","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Sparse bounds for maximal oscillatory rough singular integral operators","authors":"Surjeet Singh Choudhary ,&nbsp;Saurabh Shrivastava ,&nbsp;Kalachand Shuin","doi":"10.1016/j.bulsci.2025.103612","DOIUrl":"10.1016/j.bulsci.2025.103612","url":null,"abstract":"&lt;div&gt;&lt;div&gt;In this paper, we prove sparse bounds for the maximal oscillatory rough singular integral operator&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;⁎&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;munder&gt;&lt;mi&gt;sup&lt;/mi&gt;&lt;mrow&gt;&lt;mi&gt;ϵ&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/munder&gt;&lt;mo&gt;⁡&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;munder&gt;&lt;mo&gt;∫&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mi&gt;ϵ&lt;/mi&gt;&lt;/mrow&gt;&lt;/munder&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;ι&lt;/mi&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; where &lt;span&gt;&lt;math&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; is a real-valued polynomial on &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;×&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;∞&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; is a homogeneous function of degree zero with &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mo&gt;∫&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;. This allows us to conclude weighted &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt;-estimates for the operator &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;⁎&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/math&gt;&lt;/span&gt;. Moreover, the norm &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mo&gt;‖&lt;/mo&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;⁎&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mo&gt;‖&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; depends only on the total degree of the polynomial &lt;span&gt;&lt;math&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;, but not on the coefficients of &lt;span&gt;&lt;math&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;. Finally, we will show that these techniques also apply to obtain sparse bounds for oscillatory rough singular integral operator &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/math&gt;&lt;/spa","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"201 ","pages":"Article 103612"},"PeriodicalIF":1.3,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143682037","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}