Journal of Mathematical Analysis and Applications最新文献

{"title":"Landau-type theorems for the functions whose images contain a disc","authors":"Sambhunath Sen","doi":"10.1016/j.jmaa.2025.130068","DOIUrl":"10.1016/j.jmaa.2025.130068","url":null,"abstract":"<div><div>In this article, we obtain Landau-type theorems for holomorphic and meromorphic functions in the open unit disc of the complex plane, assuming that the image of each function contains a disc of certain radius centered at the origin.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"555 2","pages":"Article 130068"},"PeriodicalIF":1.2,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110015","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":"Matrix weights on compact and non-compact domains","authors":"Morten Nielsen ,&nbsp;Hrvoje Šikić","doi":"10.1016/j.jmaa.2025.130069","DOIUrl":"10.1016/j.jmaa.2025.130069","url":null,"abstract":"<div><div>We study Muckenhoupt <span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> conditions for matrix weights and their connections to related scalar properties for values of <em>p</em> in the range <span><math><mn>1</mn><mo>≤</mo><mi>p</mi><mo>&lt;</mo><mo>∞</mo></math></span>. Special emphasis is put on the process of diagonalisation of weights and on the role played by the domain of the matrix weight, where it is shown that there are several fundamental structural differences between weights defined on compact and non-compact domains.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"555 2","pages":"Article 130069"},"PeriodicalIF":1.2,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145159174","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":"Asymptotics of orthogonal polynomials for the Abel weight","authors":"Dušan Lj. Djukić","doi":"10.1016/j.jmaa.2025.130064","DOIUrl":"10.1016/j.jmaa.2025.130064","url":null,"abstract":"<div><div>Orthogonal polynomials <span><math><msub><mrow><mi>P</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo></math></span> with respect to the Abel weight function <span><math><msub><mrow><mi>w</mi></mrow><mrow><mi>A</mi></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mfrac><mrow><mi>x</mi></mrow><mrow><mn>2</mn><mi>sinh</mi><mo>⁡</mo><mo>(</mo><mi>π</mi><mi>x</mi><mo>)</mo></mrow></mfrac></math></span> are used for numerical summation of alternating series by means of the Abel-Plana formula. Also, they are known to be related to Bernouli and Euler numbers. In this paper we first give an integral representation for these polynomials. Then, using this representation, we investigate the asymptotic behavior of <span><math><msub><mrow><mi>P</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo></math></span> when <em>n</em> is large.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"555 2","pages":"Article 130064"},"PeriodicalIF":1.2,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110014","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 explicit values of a q-multiple zeta function at roots of unity","authors":"Takao Komatsu","doi":"10.1016/j.jmaa.2025.130065","DOIUrl":"10.1016/j.jmaa.2025.130065","url":null,"abstract":"<div><div>In this paper, we give the values of a certain kind of <em>q</em>-multiple zeta function at roots of unity. Various multiple zeta values have been proposed and studied by many researchers, but these multiple zeta values naturally arise from generalizations of Stirling numbers. It is interesting, but by no means easy, to show the values explicitly in certain cases. We give explicit formulas by using Bell polynomials, determinants, <em>r</em>-Stirling numbers, etc. The techniques used by Bachmann et al. for other multiple zeta values are also of help.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"555 2","pages":"Article 130065"},"PeriodicalIF":1.2,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110013","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 application of a discrete Sobolev inequality to discretised Kirchhoff equations","authors":"Christopher S. Goodrich","doi":"10.1016/j.jmaa.2025.130066","DOIUrl":"10.1016/j.jmaa.2025.130066","url":null,"abstract":"<div><div>We develop a discrete Sobolev inequality, and we use this inequality to analyse the nonlocal discretised Kirchhoff equation<span><span><span><math><mo>−</mo><mi>A</mi><mo>(</mo><mo>(</mo><mi>a</mi><mo>⁎</mo><mo>(</mo><mi>g</mi><mo>∘</mo><mo>|</mo><mi>Δ</mi><mi>u</mi><mo>|</mo><mo>)</mo><mo>)</mo><mo>(</mo><mi>b</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>)</mo><mo>(</mo><msup><mrow><mi>Δ</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>u</mi><mo>)</mo><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mi>λ</mi><mi>f</mi><mo>(</mo><mi>n</mi><mo>,</mo><mi>u</mi><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>)</mo><mtext>, </mtext><mi>n</mi><mo>∈</mo><mo>{</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>b</mi><mo>}</mo><mo>,</mo></math></span></span></span> where ⁎ represents a finite convolution. The equation is a discrete analogue of the classical steady-state Kirchhoff equation in one space dimension. Existence of at least one positive solution is investigated under the assumption that the equation is subject to two-point boundary data such that <span><math><mi>u</mi><mo>(</mo><mn>0</mn><mo>)</mo><mo>=</mo><mn>0</mn></math></span>. Thus, both Dirichlet and right-focal data are captured by our results. An interesting aspect of our theory is that the coefficient function <em>A</em> may be both vanishing and sign-changing.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"555 2","pages":"Article 130066"},"PeriodicalIF":1.2,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145098651","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":"Traveling wave solutions for a density-suppressed motility model with strong Allee effect","authors":"Cui Song,&nbsp;Zhi-Cheng Wang","doi":"10.1016/j.jmaa.2025.130063","DOIUrl":"10.1016/j.jmaa.2025.130063","url":null,"abstract":"<div><div>In this paper, we investigate a density-suppressed motility model with strong Allee effect. By leveraging existing results on asymptotic autonomous systems, along with Fredholm theory and the Banach fixed-point theorem, we establish the existence of bistable traveling wave solutions using a perturbation argument. This result holds when the density-suppressed sensitivity is relatively small. Finally, we validate our main results through numerical simulations and further discuss wave patterns and the sign of the wave speed as the density-suppressed sensitivity varies.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"555 2","pages":"Article 130063"},"PeriodicalIF":1.2,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145098650","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":"Range-exclusive solutions of almost automorphic differential equations","authors":"B. Es-sebbar ,&nbsp;Z. Zizi","doi":"10.1016/j.jmaa.2025.130067","DOIUrl":"10.1016/j.jmaa.2025.130067","url":null,"abstract":"<div><div>We present a unified approach to establishing the existence of almost automorphic solutions to differential equations in Banach spaces. We introduce the concept of solutions having exclusive ranges for differential equations of the form <span><math><msup><mrow><mi>u</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>=</mo><mi>f</mi><mo>(</mo><mi>t</mi><mo>,</mo><mi>u</mi><mo>)</mo></math></span> in a Banach space <em>X</em>, where <em>f</em> is almost automorphic in time <em>t</em>. The proposed methodology unifies classical techniques, covering cases where nonlinearities are globally Lipschitz with exponentially stable linear parts, as well as differential equations without global Lipschitz nonlinearities. The main result shows that, under certain conditions on <em>f</em>, every solution with an exclusive range is compactly almost automorphic. To illustrate the versatility of the developed approach, we provide several examples and applications, including a Bohr–Neugebauer type theorem and the analysis of differential equations possessing multiple and unique almost automorphic solutions.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"556 1","pages":"Article 130067"},"PeriodicalIF":1.2,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145160363","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":"Hopf bifurcation in a time-delayed multi-group SIR epidemic model for population behavior change","authors":"Toshikazu Kuniya","doi":"10.1016/j.jmaa.2025.130061","DOIUrl":"10.1016/j.jmaa.2025.130061","url":null,"abstract":"<div><div>In this study, we construct a time-delayed multi-group SIR epidemic model to discuss the impact of population behavior change on the occurrence of recurrent epidemic waves. We obtain the basic reproduction number <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> and show that if <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>≤</mo><mn>1</mn></math></span>, then the disease-free equilibrium is globally asymptotically stable, whereas if <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>&gt;</mo><mn>1</mn></math></span>, then the disease-free equilibrium is unstable and an endemic equilibrium exists. In a special two-group case, we show sufficient conditions for Hopf bifurcation and obtain index values that determine the direction, stability and period of bifurcated periodic solutions. By numerical simulation, we investigate the occurrence of periodic solutions in two groups representing an urban area and a non-urban area. We conclude that the epidemic size, response intensity of population behavior change and heterogeneity in two different groups can be the key factors of the occurrence of recurrent epidemic waves.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"555 2","pages":"Article 130061"},"PeriodicalIF":1.2,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145098649","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":"Numerical dynamics of infection-age models with logistic growth and general nonlinear incidence","authors":"Zhuzan Wang ,&nbsp;Zhanwen Yang ,&nbsp;Huiqing Xie ,&nbsp;Zhijie Chen","doi":"10.1016/j.jmaa.2025.130062","DOIUrl":"10.1016/j.jmaa.2025.130062","url":null,"abstract":"<div><div>We consider an age-structured viral dynamics model with Logistic growth and a general nonlinear incidence rate. We present the basic reproduction number of the continuous model and conduct a theoretical analysis of the model. For such a hybrid infinite-dimensional system with abstract nonlinear terms, the comprehensive numerical analysis is still pending. We address this problem by establishing a fully discrete linearly implicit scheme, and the non-negativity of the numerical scheme is confirmed by utilizing the theory of <em>M</em>-matrix. With a solvability analysis, the finite time convergence is proved for strong solutions. For long-time dynamics, by utilizing the exponential decay characteristic of the fundamental solution matrix, we established a 1-order convergence analysis for the numerical reproduction number <span><math><msubsup><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow><mrow><mi>Δ</mi><mi>t</mi></mrow></msubsup></math></span>, and further proved the 1-order convergence property of numerical equilibria. By applying linearization techniques and comparison principles, we demonstrate that the disease-free equilibrium is globally asymptotically stable when <span><math><msubsup><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow><mrow><mi>Δ</mi><mi>t</mi></mrow></msubsup><mo>&lt;</mo><mn>1</mn></math></span>, and the endemic equilibrium is locally asymptotically stable when <span><math><msubsup><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow><mrow><mi>Δ</mi><mi>t</mi></mrow></msubsup><mo>&gt;</mo><mn>1</mn></math></span>. Hence, numerical processes almost completely replicate the dynamic properties of continuous system. At last, some numerical experiments demonstrate the obtained results.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"555 2","pages":"Article 130062"},"PeriodicalIF":1.2,"publicationDate":"2025-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145098646","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":"Integral operators in the Schatten class on Dirichlet spaces","authors":"Xin-Qi Wen ,&nbsp;Cheng Yuan","doi":"10.1016/j.jmaa.2025.130060","DOIUrl":"10.1016/j.jmaa.2025.130060","url":null,"abstract":"&lt;div&gt;&lt;div&gt;We characterize three integral operators in Schatten &lt;em&gt;p&lt;/em&gt;-classes on Dirichlet spaces &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; in the unit disk &lt;span&gt;&lt;math&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; for &lt;span&gt;&lt;math&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mn&gt;0&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;mo&gt;∞&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;. The main results are threefold:&lt;ul&gt;&lt;li&gt;&lt;span&gt;(1)&lt;/span&gt;&lt;span&gt;&lt;div&gt;If &lt;span&gt;&lt;math&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;&lt;&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;mo&gt;∞&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; and &lt;em&gt;g&lt;/em&gt; is a holomorphic function in &lt;span&gt;&lt;math&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;, then the Volterra operator &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;, defined by&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;munderover&gt;&lt;mo&gt;∫&lt;/mo&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;/mrow&gt;&lt;/munderover&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;ζ&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;g&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;ζ&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mi&gt;ζ&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; is in the Schatten &lt;em&gt;p&lt;/em&gt;-class on &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; if and only if&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;munder&gt;&lt;mo&gt;∫&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;/munder&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&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;mi&gt;w&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;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;munder&gt;&lt;mo&gt;∫&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;/munder&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;g&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;mo&gt;)&lt;/mo&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;mi&gt;d&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;¯&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&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;mn&gt;2&lt;/mn&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mi&gt;α&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;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;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;msup&gt;&lt;mrow&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;mi&gt;w&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;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;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mo&gt;∞&lt;/mo&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;&lt;/span&gt;&lt;/li&gt;&lt;li&gt;&lt;span&gt;(2)&lt;/span&gt;&lt;span&gt;&lt;div&gt;If &lt;span&gt;&lt;math&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mn&gt;0&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;mo&gt;∞&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;, &lt;em&gt;μ&lt;/em&gt; is a finite Borel measure on &lt;span&gt;&lt;math&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;, then the Toeplitz operator &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;Q&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/math&gt;&lt;/span&gt; acting on &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"555 2","pages":"Article 130060"},"PeriodicalIF":1.2,"publicationDate":"2025-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145098648","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}