Journal of Mathematical Analysis and Applications最新文献

{"title":"Locally constrained flows and geometric inequalities in spheres","authors":"Shanwei Ding,&nbsp;Guanghan Li","doi":"10.1016/j.jmaa.2025.129689","DOIUrl":"10.1016/j.jmaa.2025.129689","url":null,"abstract":"<div><div>In this paper, we unveil a captivating algebraic property of an elementary symmetric polynomial. Based on this property, we establish the longtime existence and convergence of a locally constrained flow, thereby deriving some families of geometric inequalities in sphere. Additionally, we demonstrate a novel family of “three terms” geometric inequalities involving two weighted curvature integrals and one quermassintegral. Unlike the case in hyperbolic spaces, a family of inverse weighted geometric inequalities hold in spheres.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 2","pages":"Article 129689"},"PeriodicalIF":1.2,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144105149","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":"Arithmetic properties of k-tuple ℓ-regular partitions","authors":"Hemjyoti Nath ,&nbsp;Manjil P. Saikia ,&nbsp;Abhishek Sarma","doi":"10.1016/j.jmaa.2025.129688","DOIUrl":"10.1016/j.jmaa.2025.129688","url":null,"abstract":"<div><div>In this paper, we study arithmetic properties satisfied by the <em>k</em>-tuple <em>ℓ</em>-regular partitions. A <em>k</em>-tuple of partitions <span><math><mo>(</mo><msub><mrow><mi>ξ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>ξ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>ξ</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>)</mo></math></span> is said to be <em>ℓ</em>-regular if all the <span><math><msub><mrow><mi>ξ</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span>'s are <em>ℓ</em>-regular. We study the cases <span><math><mo>(</mo><mi>ℓ</mi><mo>,</mo><mi>k</mi><mo>)</mo><mo>=</mo><mo>(</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>,</mo><mo>(</mo><mn>4</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>,</mo><mo>(</mo><mi>ℓ</mi><mo>,</mo><mi>p</mi><mo>)</mo></math></span>, where <em>p</em> is a prime, and even the general case when both <em>ℓ</em> and <em>k</em> are unrestricted. Using elementary means as well as the theory of modular forms we prove several infinite family of congruences and density results for this family of partitions.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 2","pages":"Article 129688"},"PeriodicalIF":1.2,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144105155","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":"Distribution of θ-powers and their sums","authors":"Siddharth Iyer","doi":"10.1016/j.jmaa.2025.129672","DOIUrl":"10.1016/j.jmaa.2025.129672","url":null,"abstract":"<div><div>We refine a remark of Steinerberger (2024), proving that for <span><math><mi>α</mi><mo>∈</mo><mi>R</mi></math></span>, there exist integers <span><math><mn>1</mn><mo>≤</mo><msub><mrow><mi>b</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>b</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>≤</mo><mi>n</mi></math></span> such that<span><span><span><math><mrow><mo>‖</mo><munderover><mo>∑</mo><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>k</mi></mrow></munderover><msqrt><mrow><msub><mrow><mi>b</mi></mrow><mrow><mi>j</mi></mrow></msub></mrow></msqrt><mo>−</mo><mi>α</mi><mo>‖</mo></mrow><mo>=</mo><mi>O</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mo>−</mo><msub><mrow><mi>γ</mi></mrow><mrow><mi>k</mi></mrow></msub></mrow></msup><mo>)</mo><mo>,</mo></math></span></span></span> where <span><math><msub><mrow><mi>γ</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>≥</mo><mo>(</mo><mi>k</mi><mo>−</mo><mn>1</mn><mo>)</mo><mo>/</mo><mn>4</mn></math></span>, <span><math><msub><mrow><mi>γ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>=</mo><mn>1</mn></math></span>, and <span><math><msub><mrow><mi>γ</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>=</mo><mi>k</mi><mo>/</mo><mn>2</mn></math></span> for <span><math><mi>k</mi><mo>=</mo><msup><mrow><mn>2</mn></mrow><mrow><mi>m</mi></mrow></msup><mo>−</mo><mn>1</mn></math></span>. We extend this to higher-order roots. Building on the Bambah–Chowla theorem, we study gaps in <span><math><mo>{</mo><msup><mrow><mi>x</mi></mrow><mrow><mi>θ</mi></mrow></msup><mo>+</mo><msup><mrow><mi>y</mi></mrow><mrow><mi>θ</mi></mrow></msup><mo>:</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>∈</mo><mi>N</mi><mo>∪</mo><mo>{</mo><mn>0</mn><mo>}</mo><mo>}</mo></math></span>, yielding a modulo one result with <span><math><msub><mrow><mi>γ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>=</mo><mn>1</mn></math></span> and bounded gaps for <span><math><mi>θ</mi><mo>=</mo><mn>3</mn><mo>/</mo><mn>2</mn></math></span>. We also establish a metric result for general <span><math><mi>θ</mi><mo>&gt;</mo><mn>0</mn></math></span> and identify exceptional values, thereby resolving a question of Dubickas (2024).</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 1","pages":"Article 129672"},"PeriodicalIF":1.2,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144083780","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":"Perturbation limiting behaviors of ground states to the Kirchhoff equation with combined power-type nonlinearities","authors":"Deke Li","doi":"10.1016/j.jmaa.2025.129677","DOIUrl":"10.1016/j.jmaa.2025.129677","url":null,"abstract":"&lt;div&gt;&lt;div&gt;In this paper, we consider the Kirchhoff-type equation with combined power-type nonlinearities:&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;munder&gt;&lt;mo&gt;∫&lt;/mo&gt;&lt;mrow&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;/mrow&gt;&lt;/munder&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;ε&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mtext&gt;in &lt;/mtext&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;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; where &lt;span&gt;&lt;math&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;mi&gt;ε&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; are constants, &lt;span&gt;&lt;math&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;mo&gt;&lt;&lt;/mo&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;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt;. We mainly focus on the existence and perturbation limit behaviors of ground states &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;ε&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;ρ&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;, where &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;ε&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;ρ&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; is radially symmetric-decreasing and &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;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;ε&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;ρ&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;ρ&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;. Firstly, we prove the existence and nonexistence of ground states by using the concentration-compactness principle. Secondly, we characterize the perturbation limit behaviors of ground states &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;ε&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;ρ&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; as &lt;span&gt;&lt;math&gt;&lt;mi&gt;ε&lt;/mi&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; and find that the blow-up phenomenon happens for &lt;span&gt;&lt;math&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;8&lt;/mn&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;mo&gt;&lt;&lt;/mo&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;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mi&gt;ρ&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ρ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; in the sense that &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;lim&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;ε&lt;/mi&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mro","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 1","pages":"Article 129677"},"PeriodicalIF":1.2,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144068781","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":"Kernel theorems for operators on co-orbit spaces associated with localised frames","authors":"Dimitri Bytchenkoff ,&nbsp;Michael Speckbacher ,&nbsp;Peter Balazs","doi":"10.1016/j.jmaa.2025.129678","DOIUrl":"10.1016/j.jmaa.2025.129678","url":null,"abstract":"<div><div>Kernel theorems provide a convenient representation of bounded linear operators. For the operator acting on a concrete function space, this means that its action on any element of the space can be expressed as a generalised integral operator, in a way reminiscent of the matrix representation of linear operators acting on finite dimensional vector spaces. We prove kernel theorems for bounded linear operators acting on co-orbit spaces associated with localised frames. Our two main results characterise the spaces of operators whose generalised integral kernels belong to the co-orbit spaces of test functions and distributions associated with the tensor product of the localised frames respectively. Moreover, using a version of Schur's test, we establish a characterisation of the bounded linear operators between some specific co-orbit spaces and kernels in mixed-norm co-orbit spaces.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 1","pages":"Article 129678"},"PeriodicalIF":1.2,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144068780","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":"Sobolev and Hölder estimates for the ∂‾ equation on pseudoconvex domains of finite type in C2","authors":"Ziming Shi","doi":"10.1016/j.jmaa.2025.129638","DOIUrl":"10.1016/j.jmaa.2025.129638","url":null,"abstract":"<div><div>We prove a homotopy formula which yields almost sharp estimates in all (positive-indexed) Sobolev and Hölder-Zygmund spaces for the <span><math><mover><mrow><mo>∂</mo></mrow><mo>‾</mo></mover></math></span> equation on pseudoconvex domains of finite type in <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>, extending the earlier results of Fefferman-Kohn (1988), Range (1990), and Chang-Nagel-Stein (1992). The main novelty of our proof is the construction of holomorphic support functions that admit precise estimates when the parameter variable lies in a thin shell outside the domain.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 1","pages":"Article 129638"},"PeriodicalIF":1.2,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144147965","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 a product of three theta functions and the number of representations of integers as mixed ternary sums involving squares, triangular, pentagonal and octagonal numbers","authors":"Nasser Abdo Saeed Bulkhali ,&nbsp;Gedela Kavya Keerthana ,&nbsp;Ranganatha Dasappa","doi":"10.1016/j.jmaa.2025.129676","DOIUrl":"10.1016/j.jmaa.2025.129676","url":null,"abstract":"<div><div>In this paper, we derive a general formula to express the product of three theta functions as a linear combination of other products of three theta functions. Moreover, we use the main formula to deduce a general formula for the product of two theta functions. Furthermore, as applications, we extract several theorems in the theory of representation of integers as mixed ternary sums involving squares, triangular numbers, generalized pentagonal numbers and generalized octagonal numbers.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 2","pages":"Article 129676"},"PeriodicalIF":1.2,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144090558","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":"Fractional Hardy's inequality for half-spaces in the Heisenberg group","authors":"Rama Rawat,&nbsp;Haripada Roy","doi":"10.1016/j.jmaa.2025.129674","DOIUrl":"10.1016/j.jmaa.2025.129674","url":null,"abstract":"&lt;div&gt;&lt;div&gt;We establish the following fractional Hardy's inequality&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;munder&gt;&lt;mo&gt;∫&lt;/mo&gt;&lt;mrow&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/mrow&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;/msubsup&gt;&lt;/mrow&gt;&lt;/munder&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;ξ&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mi&gt;ξ&lt;/mi&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;munder&gt;&lt;mo&gt;∫&lt;/mo&gt;&lt;mrow&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/mrow&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;/msubsup&gt;&lt;/mrow&gt;&lt;/munder&gt;&lt;munder&gt;&lt;mo&gt;∫&lt;/mo&gt;&lt;mrow&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/mrow&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;/msubsup&gt;&lt;/mrow&gt;&lt;/munder&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;ξ&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;ξ&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;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;ξ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&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;msup&gt;&lt;mrow&gt;&lt;mi&gt;ξ&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;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;Q&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;z&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;mi&gt;z&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;ξ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;′&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mi&gt;ξ&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mo&gt;∀&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/mrow&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;/msubsup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; for the half-space &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/mrow&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;/msubsup&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mi&gt;ξ&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;x&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;mo&gt;…&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;y&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;mo&gt;…&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;H&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;msub&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; in the Heisenberg group &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;H&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; under the conditions &lt;span&gt;&lt;math&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mo","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 1","pages":"Article 129674"},"PeriodicalIF":1.2,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144089765","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":"Refinements of Van Hamme's (E.2) and (F.2) supercongruences and two supercongruences by Swisher","authors":"Victor J.W. Guo ,&nbsp;Chen Wang","doi":"10.1016/j.jmaa.2025.129673","DOIUrl":"10.1016/j.jmaa.2025.129673","url":null,"abstract":"<div><div>In 1997, Van Hamme proposed 13 supercongruences on truncated hypergeometric series. Van Hamme's (B.2) supercongruence was first confirmed by Mortenson and received a WZ proof by Zudilin later. In 2012, using the WZ method again, Sun extended Van Hamme's (B.2) supercongruence to the modulus <span><math><msup><mrow><mi>p</mi></mrow><mrow><mn>4</mn></mrow></msup></math></span> case, where <em>p</em> is an odd prime. In this paper, by using a more general WZ pair, we generalize Hamme's (E.2) and (F.2) supercongruences, as well as two supercongruences by Swisher, to the modulus <span><math><msup><mrow><mi>p</mi></mrow><mrow><mn>4</mn></mrow></msup></math></span> case. Our generalizations of these supercongruences are related to Euler polynomials. We also put forward a relevant conjecture on a <em>q</em>-supercongruence for further study.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 1","pages":"Article 129673"},"PeriodicalIF":1.2,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144089764","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":"Hausdorff operators on weighted Bergman and Hardy spaces","authors":"Ha Duy Hung ,&nbsp;Luong Dang Ky","doi":"10.1016/j.jmaa.2025.129661","DOIUrl":"10.1016/j.jmaa.2025.129661","url":null,"abstract":"<div><div>Let <span><math><mn>1</mn><mo>≤</mo><mi>p</mi><mo>&lt;</mo><mo>∞</mo></math></span>, <span><math><mi>α</mi><mo>&gt;</mo><mo>−</mo><mn>1</mn></math></span>, and let <em>φ</em> be a measurable function on <span><math><mo>(</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo></math></span>. The main purpose of this paper is to study the Hausdorff operator<span><span><span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>φ</mi></mrow></msub><mi>f</mi><mo>(</mo><mi>z</mi><mo>)</mo><mo>=</mo><munderover><mo>∫</mo><mrow><mn>0</mn></mrow><mrow><mo>∞</mo></mrow></munderover><mi>f</mi><mrow><mo>(</mo><mfrac><mrow><mi>z</mi></mrow><mrow><mi>t</mi></mrow></mfrac><mo>)</mo></mrow><mfrac><mrow><mi>φ</mi><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mrow><mi>t</mi></mrow></mfrac><mi>d</mi><mi>t</mi><mo>,</mo><mspace></mspace><mi>z</mi><mo>∈</mo><msup><mrow><mi>C</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>,</mo></math></span></span></span> on the weighted Bergman space <span><math><msubsup><mrow><mi>A</mi></mrow><mrow><mi>α</mi></mrow><mrow><mi>p</mi></mrow></msubsup><mo>(</mo><msub><mrow><mi>C</mi></mrow><mrow><mo>+</mo></mrow></msub><mo>)</mo></math></span> and on the power weighted Hardy space <span><math><msubsup><mrow><mi>H</mi></mrow><mrow><mo>|</mo><mo>⋅</mo><msup><mrow><mo>|</mo></mrow><mrow><mi>α</mi></mrow></msup></mrow><mrow><mi>p</mi></mrow></msubsup><mo>(</mo><msub><mrow><mi>C</mi></mrow><mrow><mo>+</mo></mrow></msub><mo>)</mo></math></span> of the upper half-plane. Some applications to the real version of <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>φ</mi></mrow></msub></math></span> are also given.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 1","pages":"Article 129661"},"PeriodicalIF":1.2,"publicationDate":"2025-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144068779","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}