Journal of Mathematical Analysis and Applications最新文献

{"title":"Value distribution of a pair of meromorphic functions","authors":"","doi":"10.1016/j.jmaa.2024.128914","DOIUrl":"10.1016/j.jmaa.2024.128914","url":null,"abstract":"<div><div>The well-known Picard theorem shows only what happens on the Picard exceptional value of a meromorphic function <em>f</em>. In this paper, we mainly consider what happens on the common or different Picard exceptional values of two or three meromorphic functions with certain types. For instance, we will provide some new results and discussions for the generalized Picard exceptional values or small functions of a pair of meromorphic functions <span><math><msup><mrow><mi>f</mi></mrow><mrow><mi>n</mi></mrow></msup><msup><mrow><mi>g</mi></mrow><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup></math></span> and <span><math><msup><mrow><mi>g</mi></mrow><mrow><mi>m</mi></mrow></msup><msup><mrow><mi>f</mi></mrow><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></msup></math></span>, these two functions are the crossed variants of the complex differential polynomials in Hayman's conjecture, where <em>n</em>, <em>m</em> are positive integers and <span><math><mi>k</mi><mo>≥</mo><mn>0</mn></math></span>. We give more details on the case that <span><math><mi>f</mi><msup><mrow><mi>g</mi></mrow><mrow><mo>′</mo></mrow></msup></math></span> and <span><math><mi>g</mi><msup><mrow><mi>f</mi></mrow><mrow><mo>′</mo></mrow></msup></math></span> when <em>f</em> and <em>g</em> are exponential polynomials in particular.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142327393","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 Matoušek-like embedding obstructions of countably branching graphs","authors":"","doi":"10.1016/j.jmaa.2024.128896","DOIUrl":"10.1016/j.jmaa.2024.128896","url":null,"abstract":"<div><div>In this paper we present new proofs of the non-embeddability of countably branching trees into Banach spaces satisfying property <span><math><mo>(</mo><msub><mrow><mi>β</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>)</mo></math></span> and of countably branching diamonds into Banach spaces which are <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>-asymptotic midpoint uniformly convex (<em>p</em>-AMUC) for <span><math><mi>p</mi><mo>&gt;</mo><mn>1</mn></math></span>. These proofs are entirely metric in nature and are inspired by previous work of Jiří Matoušek. In addition, using this metric method, we succeed in extending these results to metric spaces satisfying certain embedding obstruction inequalities. Finally, we give Tessera-type lower bounds on the compression for a class of Lipschitz embeddings of the countably branching trees into Banach spaces containing <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>-asymptotic models for <span><math><mi>p</mi><mo>≥</mo><mn>1</mn></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142318880","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":"Positive multi-bump solutions for the Schrödinger equation with slow decaying competing potentials","authors":"","doi":"10.1016/j.jmaa.2024.128904","DOIUrl":"10.1016/j.jmaa.2024.128904","url":null,"abstract":"&lt;div&gt;&lt;div&gt;We are concerned with the existence of multi-bump solutions to the following nonlinear Schrödinger equation with competing potentials &lt;em&gt;V&lt;/em&gt; and &lt;em&gt;Q&lt;/em&gt;,&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;V&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;mo&gt;)&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;Q&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;mo&gt;)&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;u&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;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mtext&gt;in&lt;/mtext&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mspace&gt;&lt;/mspace&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;/mrow&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; where &lt;span&gt;&lt;math&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&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;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/math&gt;&lt;/span&gt;, &lt;em&gt;V&lt;/em&gt; and &lt;em&gt;Q&lt;/em&gt; are radial functions having the following slow algebraic decay with &lt;span&gt;&lt;math&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;n&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;span&gt;&lt;span&gt;&lt;math&gt;&lt;mi&gt;V&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;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;O&lt;/mi&gt;&lt;mrow&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;mo&gt;|&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;κ&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;Q&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;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;Q&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;x&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;mo&gt;+&lt;/mo&gt;&lt;mi&gt;O&lt;/mi&gt;&lt;mrow&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;mo&gt;|&lt;/mo&gt;&lt;mi&gt;x&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;mo&gt;+&lt;/mo&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mtext&gt; as &lt;/mtext&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;mtext&gt;,&lt;/mtext&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;Q&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;κ&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&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;. By introducing a weighted norm and some delicate analysis, we construct infinitely many new positive multi-bump solutions for &lt;span&gt;&lt;math&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; or &lt;span&gt;&lt;math&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;. The maximum points of these bump solutions lie on the top and bottom circles of a cylinder near the infinity. This result complements and extends the existence results of multi-bump solutions in &lt;span&gt;&lt;span&gt;[2]&lt;/span&gt;&lt;/span&gt;, &lt;s","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142318879","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 properties of new sequence spaces based on Riordan numbers","authors":"","doi":"10.1016/j.jmaa.2024.128902","DOIUrl":"10.1016/j.jmaa.2024.128902","url":null,"abstract":"<div><div>In this paper, we define a new class of sequence spaces via Riordan numbers and prove their topological properties, and inclusion relations, obtain Schauder basis, and describe <span><math><mi>α</mi><mo>,</mo><mi>β</mi></math></span> and <em>γ</em> duals of them. We have given conditions under which there is matrix transformation between those new sequence spaces and the well-known classical sequence spaces. In the last part, we are given some results related to some special operator classes, such as approximable operators, nuclear operators, and ideal operators.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142318877","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 Haagerup noncommutative quasi Hp(A) spaces","authors":"","doi":"10.1016/j.jmaa.2024.128905","DOIUrl":"10.1016/j.jmaa.2024.128905","url":null,"abstract":"<div><div>Let <span><math><mi>M</mi></math></span> be a <em>σ</em>-finite von Neumann algebra, equipped with a normal faithful state <em>φ</em>, and let <span><math><mi>A</mi></math></span> be a maximal subdiagonal subalgebra of <span><math><mi>M</mi></math></span>. We have proved that for <span><math><mn>0</mn><mo>&lt;</mo><mi>p</mi><mo>&lt;</mo><mn>1</mn></math></span>, <span><math><msup><mrow><mi>H</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><mi>A</mi><mo>)</mo></math></span> is independent of <em>φ</em>. Furthermore, in the case that <span><math><mi>A</mi></math></span> is a type 1 subdiagonal subalgebra, we have obtained an interpolation theorem for <span><math><msup><mrow><mi>H</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><mi>A</mi><mo>)</mo></math></span> in the case where <span><math><mn>0</mn><mo>&lt;</mo><mi>θ</mi><mo>&lt;</mo><mn>1</mn></math></span>, <span><math><mn>0</mn><mo>&lt;</mo><msub><mrow><mi>p</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><msub><mrow><mi>p</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>≤</mo><mo>∞</mo></math></span> and <span><math><mi>p</mi><mo>=</mo><mfrac><mrow><mn>1</mn><mo>−</mo><mi>θ</mi></mrow><mrow><msub><mrow><mi>p</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></mfrac><mo>+</mo><mfrac><mrow><mi>θ</mi></mrow><mrow><msub><mrow><mi>p</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></mfrac><mo>≥</mo><mn>1</mn></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142324154","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":"Approximation orders of real numbers in beta-dynamical systems","authors":"","doi":"10.1016/j.jmaa.2024.128895","DOIUrl":"10.1016/j.jmaa.2024.128895","url":null,"abstract":"<div><div>For any real numbers <span><math><mi>x</mi><mo>∈</mo><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span> and <span><math><mi>β</mi><mo>&gt;</mo><mn>1</mn></math></span>, denote by <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>x</mi><mo>,</mo><mi>β</mi><mo>)</mo></math></span> the partial sum of the first <em>n</em> terms in the <em>β</em>-expansion of <em>x</em>. It is known that for any <span><math><mi>β</mi><mo>&gt;</mo><mn>1</mn></math></span> and almost all <span><math><mi>x</mi><mo>∈</mo><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span>, or for any <span><math><mi>x</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span> and almost all <span><math><mi>β</mi><mo>&gt;</mo><mn>1</mn></math></span>, the approximation order of <em>x</em> by <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>x</mi><mo>,</mo><mi>β</mi><mo>)</mo></math></span> is <span><math><msup><mrow><mi>β</mi></mrow><mrow><mo>−</mo><mi>n</mi></mrow></msup></math></span>. Let <span><math><mi>φ</mi><mo>:</mo><mi>N</mi><mo>→</mo><msup><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msup></math></span> be a positive function. In this paper, we study the Hausdorff dimensions of the following two sets<span><span><span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>β</mi></mrow></msub><mo>(</mo><mi>φ</mi><mo>)</mo><mo>=</mo><mrow><mo>{</mo><mi>x</mi><mo>∈</mo><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo><mo>:</mo><munder><mrow><mrow><mi>lim</mi></mrow><mspace></mspace><mrow><mi>sup</mi></mrow></mrow><mrow><mi>n</mi><mo>→</mo><mo>∞</mo></mrow></munder><mspace></mspace><mfrac><mrow><msub><mrow><mi>log</mi></mrow><mrow><mi>β</mi></mrow></msub><mo>⁡</mo><mo>(</mo><mi>x</mi><mo>−</mo><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>x</mi><mo>,</mo><mi>β</mi><mo>)</mo><mo>)</mo></mrow><mrow><mi>φ</mi><mo>(</mo><mi>n</mi><mo>)</mo></mrow></mfrac><mo>=</mo><mo>−</mo><mn>1</mn><mo>}</mo></mrow><mo>,</mo><msub><mrow><mi>A</mi></mrow><mrow><mi>x</mi></mrow></msub><mo>(</mo><mi>φ</mi><mo>)</mo><mo>=</mo><mrow><mo>{</mo><mi>β</mi><mo>&gt;</mo><mn>1</mn><mo>:</mo><munder><mrow><mrow><mi>lim</mi></mrow><mspace></mspace><mrow><mi>sup</mi></mrow></mrow><mrow><mi>n</mi><mo>→</mo><mo>∞</mo></mrow></munder><mspace></mspace><mfrac><mrow><msub><mrow><mi>log</mi></mrow><mrow><mi>β</mi></mrow></msub><mo>⁡</mo><mo>(</mo><mi>x</mi><mo>−</mo><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>x</mi><mo>,</mo><mi>β</mi><mo>)</mo><mo>)</mo></mrow><mrow><mi>φ</mi><mo>(</mo><mi>n</mi><mo>)</mo></mrow></mfrac><mo>=</mo><mo>−</mo><mn>1</mn><mo>}</mo></mrow><mo>,</mo></math></span></span></span> and complement the dimension theoretic results of these sets in <span><span>[3]</span></span>, <span><span>[6]</span></span> and <span><span>[18]</span></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142324040","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":"An invariant for affine maximal type equations","authors":"","doi":"10.1016/j.jmaa.2024.128898","DOIUrl":"10.1016/j.jmaa.2024.128898","url":null,"abstract":"<div><div>Let <span><math><mi>y</mi><mo>:</mo><mi>M</mi><mo>→</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup></math></span> be a locally strongly convex hypersurface immersion of a smooth, connected manifold into the real affine space <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup></math></span>, given as the graph of a smooth, strictly convex function <span><math><msub><mrow><mi>x</mi></mrow><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>=</mo><mi>f</mi><mo>(</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>,</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></math></span> defined on a domain <span><math><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>. Considering the <em>α</em>-relative normalization of the graph of the convex function <em>f</em>, we will prove a Bernstein theorem for a class of nonlinear, fourth order partial differential equations of affine maximal type. As applications, we define an invariant of the equations and prove a rigidity result of the complete <span><math><msup><mrow><mi>T</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>-invariant Kähler metric on complex torus <span><math><msup><mrow><mo>(</mo><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>)</mo></mrow><mrow><mi>n</mi></mrow></msup></math></span> with vanishing scalar curvature for <span><math><mi>n</mi><mo>≤</mo><mn>5</mn></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142318878","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 kernel functions of Dirichlet spaces","authors":"","doi":"10.1016/j.jmaa.2024.128897","DOIUrl":"10.1016/j.jmaa.2024.128897","url":null,"abstract":"<div><div>For a planar domain Ω, we consider the Dirichlet spaces with respect to a base point <span><math><mi>ζ</mi><mo>∈</mo><mi>Ω</mi></math></span> and the corresponding kernel functions. It is not known how these kernel functions behave as we vary the base point. In this note, we prove that these kernel functions vary smoothly. As an application of the smoothness result, we prove a Ramadanov-type theorem for these kernel functions on <span><math><mi>Ω</mi><mo>×</mo><mi>Ω</mi></math></span>. This extends the previously known convergence results of these kernel functions. In fact, we have made these observations in a more general setting, that is, for weighted kernel functions and their higher-order counterparts.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142318876","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 norm attaining Bloch maps","authors":"","doi":"10.1016/j.jmaa.2024.128901","DOIUrl":"10.1016/j.jmaa.2024.128901","url":null,"abstract":"<div><div>Given a complex Banach space <em>X</em>, let <span><math><mover><mrow><mi>B</mi></mrow><mrow><mo>ˆ</mo></mrow></mover><mo>(</mo><mi>D</mi><mo>,</mo><mi>X</mi><mo>)</mo></math></span> denote the space of all normalized Bloch maps from the open complex unit disc <span><math><mi>D</mi></math></span> into <em>X</em>. We prove that the set of all maps in <span><math><mover><mrow><mi>B</mi></mrow><mrow><mo>ˆ</mo></mrow></mover><mo>(</mo><mi>D</mi><mo>,</mo><mi>X</mi><mo>)</mo></math></span> which attain their Bloch norms is norm dense in <span><math><mover><mrow><mi>B</mi></mrow><mrow><mo>ˆ</mo></mrow></mover><mo>(</mo><mi>D</mi><mo>,</mo><mi>X</mi><mo>)</mo></math></span>. Our approach is based on a previous study of the extremal structure of the unit closed ball of <span><math><mi>G</mi><mo>(</mo><mi>D</mi><mo>)</mo></math></span> (the Bloch-free Banach space over <span><math><mi>D</mi></math></span>). We prove that normalized Bloch atoms of <span><math><mi>D</mi></math></span> are precisely the only extreme points of that ball and, in fact, they are strongly exposed points. Moreover, we characterize the surjective linear isometries of <span><math><mi>G</mi><mo>(</mo><mi>D</mi><mo>)</mo></math></span> involved the Möbius transformations of <span><math><mi>D</mi></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142315098","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":"Two parameterized deformed Poisson type operator and the combinatorial moment formula","authors":"","doi":"10.1016/j.jmaa.2024.128888","DOIUrl":"10.1016/j.jmaa.2024.128888","url":null,"abstract":"<div><div>In this paper, we shall introduce two parameterized deformation of the classical Poisson random variable from the viewpoint of noncommutative probability, namely <span><math><mo>(</mo><mi>q</mi><mo>,</mo><mi>s</mi><mo>)</mo></math></span>-Poisson type operator (random variable) on the two parameterized deformed Fock space, namely, the <span><math><mo>(</mo><mi>q</mi><mo>,</mo><mi>s</mi><mo>)</mo></math></span>-Fock space constructed by the weighted <em>q</em>-deformation approach in <span><span>[11]</span></span>, <span><span>[4]</span></span> (see also <span><span>[6]</span></span>). The recurrence formula for the orthogonal polynomials of the <span><math><mo>(</mo><mi>q</mi><mo>,</mo><mi>s</mi><mo>)</mo></math></span>-deformed Poisson distribution is determined. Moreover we shall also give the combinatorial moment formula of the <span><math><mo>(</mo><mi>q</mi><mo>,</mo><mi>s</mi><mo>)</mo></math></span>-Poisson type operator by using the set partitions and the card arrangement technique with their statistics. Our method presented in this paper provides nice combinatorial interpretations to parameters, <em>q</em> and <em>s</em>. The deformation presented in this paper can be regarded as a generalization of the Al-Salam-Carlitz type, because the restricted case <span><math><mi>s</mi><mo>=</mo><mi>q</mi></math></span> recovers the <em>q</em>-Charlier polynomials of Al-Salam-Carlitz type appeared in combinatorics <span><span>[17]</span></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142319715","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}