Bulletin des Sciences Mathematiques最新文献

{"title":"Weighted Hardy factorizations in terms of Multilinear Calderón-Zygmund and fractional integral operators","authors":"Suting Zheng ,&nbsp;Dinghuai Wang ,&nbsp;Lisheng Shu","doi":"10.1016/j.bulsci.2024.103507","DOIUrl":"10.1016/j.bulsci.2024.103507","url":null,"abstract":"<div><p>The foundational paper of Coifman-Rochberg-Weiss provided a constructive proof of the weak factorizations of the classical Hardy space in terms of Riesz transforms. In this paper, we establish the factorization theorems for the weighted Hardy spaces. The results are also extended to the multilinear setting. Furthermore, we show that the weighted <em>BMO</em> space and weighted Lipschitz spaces are necessary for the weighted boundedness of commutators of the multilinear Calderón-Zygmund and fractional integral operators, respectively.</p></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"197 ","pages":"Article 103507"},"PeriodicalIF":1.3,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142150658","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":"Mixed radial-angular integrabilities for commutators of fractional Hardy operators","authors":"Ronghui Liu ,&nbsp;Shuangping Tao ,&nbsp;Huoxiong Wu","doi":"10.1016/j.bulsci.2024.103506","DOIUrl":"10.1016/j.bulsci.2024.103506","url":null,"abstract":"&lt;div&gt;&lt;p&gt;In this paper, we introduce the mixed radial-angular homogeneous CMO spaces &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;CMO&lt;/mi&gt;&lt;/mrow&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;rad&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msub&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;/msub&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;ang&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/msubsup&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;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; and the mixed radial-angular Herz spaces &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;K&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;˙&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;rad&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msub&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;/msub&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;ang&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&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;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;, respectively. Furthermore, the boundedness of commutators &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; generated by the fractional Hardy operators &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; with a function &lt;em&gt;b&lt;/em&gt; in &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;CMO&lt;/mi&gt;&lt;/mrow&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;rad&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msub&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;/msub&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;ang&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/msubsup&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;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; are established on &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;K&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;˙&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;rad&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msub&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;/msub&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;ang&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&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;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;. Meanwhile, the corresponding results for &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; when &lt;span&gt;&lt;math&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;CMO&lt;/mi&gt;&lt;/mrow&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;rad&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msub&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;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;ang&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/msubsup&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;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;, the mixed radial-angular homogeneous &lt;em&gt;λ&lt;/","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"197 ","pages":"Article 103506"},"PeriodicalIF":1.3,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142150662","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":"Chow forms and complete intersections in the projective space","authors":"Michel Méo","doi":"10.1016/j.bulsci.2024.103505","DOIUrl":"10.1016/j.bulsci.2024.103505","url":null,"abstract":"<div><p>We prove that every Hodge cohomology class of bidegree <span><math><mo>(</mo><mi>q</mi><mo>,</mo><mi>q</mi><mo>)</mo></math></span> on a projective manifold <em>X</em> can be recovered from its image by the Chow transformation restricted to a suitable irreducible algebraic component of the space <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>q</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span> of effective algebraic cycles in <em>X</em> of dimension <span><math><mi>q</mi><mo>−</mo><mn>1</mn></math></span>. An application to the problem of the approximation by algebraic cycles is given. In the case of the cohomology class of an effective algebraic cycle, this injectivity at the cohomological level is a consequence of the inversion formula for the Chow transform of a conormal. When <span><math><mi>X</mi><mo>=</mo><msub><mrow><mi>P</mi></mrow><mrow><mi>N</mi></mrow></msub></math></span>, the inversion formula for the conormal is extended to the case of the conormal of any closed positive <span><math><mo>(</mo><mi>q</mi><mo>,</mo><mi>q</mi><mo>)</mo></math></span>-current. An inversion formula for the Radon transform, defined on the Grassmannian, of smooth functions is involved and is also used to obtain a characterization of Chow forms of complete intersections in the projective space, expressed by means of the Capelli differential operators.</p></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"197 ","pages":"Article 103505"},"PeriodicalIF":1.3,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142137452","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 Leibniz type rule for generalized fractional derivatives","authors":"Wael Abdelhedi","doi":"10.1016/j.bulsci.2024.103495","DOIUrl":"10.1016/j.bulsci.2024.103495","url":null,"abstract":"<div><p>In this paper, we present a new Leibniz-type rule for two variants of the most generalized fractional derivatives; the regularized <em>ψ</em>-Hilfer derivative and the <span><math><mo>(</mo><mi>k</mi><mo>,</mo><mi>ψ</mi><mo>)</mo></math></span>-Hilfer derivative. As a special case, we recover the Leibniz-type rule associated to some well known fractional derivatives.</p></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"196 ","pages":"Article 103495"},"PeriodicalIF":1.3,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142077427","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":"Absolutely split locally free sheaves on proper k-schemes and Brauer–Severi varieties","authors":"Saša Novaković","doi":"10.1016/j.bulsci.2024.103494","DOIUrl":"10.1016/j.bulsci.2024.103494","url":null,"abstract":"<div><p>We classify absolutely split vector bundles on proper <em>k</em>-schemes. More precise, we prove that the closed points of the Picard scheme are in one-to-one correspondence with indecomposable absolutely split vector bundles. Furthermore, we apply the obtained results to study the geometry of (generalized) Brauer–Severi varieties.</p></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"197 ","pages":"Article 103494"},"PeriodicalIF":1.3,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S000744972400112X/pdfft?md5=9ccf4a9a1b5dc90a9bf41f334c0ecffe&pid=1-s2.0-S000744972400112X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142162453","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A generalized Bogdanov-Takens system with arbitrary degree","authors":"Hebai Chen ,&nbsp;Dehong Dai ,&nbsp;Yuhao Meng ,&nbsp;Zhaoxia Wang","doi":"10.1016/j.bulsci.2024.103491","DOIUrl":"10.1016/j.bulsci.2024.103491","url":null,"abstract":"<div><p>The aim of this paper is to give the bifurcation diagram and all global phase portraits in the Poincaré disc of a generalized Bogdanov-Takens system with arbitrary degree. Moreover, the system has abundant nonlinear phenomena, such as double limit cycle bifurcation, Hopf bifurcation, homoclinic bifurcation, heteroclinic bifurcation, and so on. Notice that the nonlinear phenomena of the system are more abundant and more complex than the classic Bogdanov-Takens system.</p></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"196 ","pages":"Article 103491"},"PeriodicalIF":1.3,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142013008","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":"The relation between μ-dichotomy spectrum and Sacker-Sell spectrum","authors":"Mengda Wu ,&nbsp;Manuel Pinto ,&nbsp;Yonghui Xia","doi":"10.1016/j.bulsci.2024.103493","DOIUrl":"10.1016/j.bulsci.2024.103493","url":null,"abstract":"<div><p>We present a relation between <em>μ</em>-dichotomy spectrum and Sacker-Sell spectrum. From this relation, we show that, under some suitable conditions, if the system <span><math><msup><mrow><mi>x</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>=</mo><mi>A</mi><mo>(</mo><mi>t</mi><mo>)</mo><mi>x</mi></math></span> admits a <em>μ</em>-dichotomy, then it admits an exponential dichotomy. Utilizing this result, we present a linearization theorem. Furthermore, we prove that the <em>μ</em>-dichotomy spectrum of the system <span><math><msup><mrow><mi>x</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>=</mo><mrow><mi>diag</mi></mrow><mo>(</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mi>t</mi><mo>)</mo><mo>,</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi>t</mi><mo>)</mo><mo>)</mo><mi>x</mi></math></span> is the union of <em>μ</em>-dichotomy spectra of the subsystems <span><math><msubsup><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow><mrow><mo>′</mo></mrow></msubsup><mo>=</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mi>t</mi><mo>)</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <span><math><msubsup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow><mrow><mo>′</mo></mrow></msubsup><mo>=</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi>t</mi><mo>)</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>, while this result is wrong if we replace <em>μ</em>-dichotomy spectrum with nonuniform exponential dichotomy spectrum. We also provide a new method to prove the <em>μ</em>-dichotomy spectral theorem.</p></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"196 ","pages":"Article 103493"},"PeriodicalIF":1.3,"publicationDate":"2024-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142077527","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 note on expansions of q-exponential equations and q-Hardy–Hille type formulas","authors":"Jian Cao ,&nbsp;Qi Bao ,&nbsp;Sama Arjika","doi":"10.1016/j.bulsci.2024.103489","DOIUrl":"10.1016/j.bulsci.2024.103489","url":null,"abstract":"<div><p>By using noncommutative <em>q</em>-analogue of binomial theorem, we construct new <em>q</em>-exponential operators for <em>q</em>-Laguerre polynomials and deduce expansions of <em>q</em>-exponential equations, which lead us to use a systematic method for studying summations and integrals involving <em>q</em>-Laguerre polynomials, such as the Rogers formula, Hardy–Hille formula, mixed-type, <span><math><mi>U</mi><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></math></span> type generating functions for <em>q</em>-Laguerre polynomials and transformational identity. We generalize some results of [Sci. China Math. <strong>66</strong>(2023), 1199–1216] and [Adv. Math. <strong>131</strong>(1997), 93–187].</p></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"195 ","pages":"Article 103489"},"PeriodicalIF":1.3,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141953338","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":"Carleson measures on bounded C-convex domains","authors":"Enchao Bi ,&nbsp;Guicong Su ,&nbsp;Shuo Zhang","doi":"10.1016/j.bulsci.2024.103492","DOIUrl":"10.1016/j.bulsci.2024.103492","url":null,"abstract":"<div><p>In this paper, we completely characterize the Carleson and the vanishing Carleson measures on bounded <span><math><mi>C</mi></math></span>-convex domains in terms of the Carathéodory (or the Kobayashi) geometry and Bergman geometry. As a corollary, we obtain a sufficient and necessary condition for the composition operators on <span><math><mi>C</mi></math></span>-convex domains to be bounded on associated Bergman spaces.</p></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"196 ","pages":"Article 103492"},"PeriodicalIF":1.3,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141942841","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 strong growth conditions for weighted spaces of entire functions","authors":"Gerhard Schindl","doi":"10.1016/j.bulsci.2024.103490","DOIUrl":"10.1016/j.bulsci.2024.103490","url":null,"abstract":"<div><p>We characterize the inclusion relations between weighted classes of entire functions with rapid decreasing growth and study strong growth comparison relations between given weights. In our considerations first we focus on weights defined in terms of the so-called associated weight function where the weight (system) is based on a given sequence. Then the abstract weight function case is reduced to the weight sequence setting by using the so-called associated weight sequence. Finally, we compare weighted entire function spaces defined in terms of so-called dilatation-type and exponential-type weight systems.</p></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"196 ","pages":"Article 103490"},"PeriodicalIF":1.3,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0007449724001088/pdfft?md5=ba79a17a44f59711dfe39409b76713b0&pid=1-s2.0-S0007449724001088-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141984973","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}