Mathematische Nachrichten最新文献

{"title":"Mean Transforms of Unbounded Weighted Composition Operator Pairs","authors":"Jing-Bin Zhou, Shihai Yang","doi":"10.1002/mana.70233","DOIUrl":"https://doi.org/10.1002/mana.70233","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we first characterize the polar decomposition of unbounded weighted composition operator pairs <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>C</mi>\u0000 <mrow>\u0000 <mi>ϕ</mi>\u0000 <mo>,</mo>\u0000 <mi>ω</mi>\u0000 </mrow>\u0000 </msub>\u0000 <annotation>${bf C}_{phi,omega }$</annotation>\u0000 </semantics></math> in an <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <annotation>$L^2$</annotation>\u0000 </semantics></math>-space. Based on this characterization, we introduce the <span></span><math>\u0000 <semantics>\u0000 <mi>λ</mi>\u0000 <annotation>$lambda$</annotation>\u0000 </semantics></math>-spherical mean transform <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>M</mi>\u0000 <mi>λ</mi>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>C</mi>\u0000 <mrow>\u0000 <mi>ϕ</mi>\u0000 <mo>,</mo>\u0000 <mi>ω</mi>\u0000 </mrow>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$mathcal {M}_lambda ({bf C}_{phi,omega })$</annotation>\u0000 </semantics></math> for <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>λ</mi>\u0000 <mo>∈</mo>\u0000 <mo>[</mo>\u0000 <mn>0</mn>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 <mo>]</mo>\u0000 </mrow>\u0000 <annotation>$lambda in [0,1]$</annotation>\u0000 </semantics></math>. We then investigate the dense definiteness of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>M</mi>\u0000 <mi>λ</mi>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>C</mi>\u0000 <mrow>\u0000 <mi>ϕ</mi>\u0000 <mo>,</mo>\u0000 <mi>ω</mi>\u0000 </mrow>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$mathcal {M}_lambda ({bf C}_{phi,omega })$</annotation>\u0000 </semantics></math>. As an application, we provide an example of a <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>-hyponorm","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 10","pages":"3139-3180"},"PeriodicalIF":1.0,"publicationDate":"2026-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149100131","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":"Eigenvalue Homogenization for the \u0000 \u0000 p\u0000 $p$\u0000 -Laplacian With Rapidly Oscillating \u0000 \u0000 \u0000 L\u0000 q\u0000 \u0000 $L^q$\u0000 Weights","authors":"Ariel Salort","doi":"10.1002/mana.70231","DOIUrl":"https://doi.org/10.1002/mana.70231","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we study the convergence rates of variational eigenvalues of the <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>-Laplacian with rapidly oscillating weights and potentials belonging in a suitable <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mi>q</mi>\u0000 </msup>\u0000 <annotation>$L^q$</annotation>\u0000 </semantics></math> space. Our analysis covers both Dirichlet and Neumann boundary conditions, and we derive explicit estimates in terms of the eigenvalue index <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 <mo>∈</mo>\u0000 <mi>N</mi>\u0000 </mrow>\u0000 <annotation>$k in mathbb {N}$</annotation>\u0000 </semantics></math> and the oscillation parameter <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>ε</mi>\u0000 <mo>&gt;</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$varepsilon &gt; 0$</annotation>\u0000 </semantics></math>. These results are obtained through a detailed examination of certain oscillatory integrals and extend previously known results in the literature.</p></div>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 10","pages":"3107-3125"},"PeriodicalIF":1.0,"publicationDate":"2026-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149100385","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":"Well-Posedness and Blow-Up Results for a p(x)-Laplacian Viscoelastic Wave Equation With Logarithmic Source Term","authors":"Mohammad Shahrouzi,&nbsp;Faramarz Tahamtani,&nbsp;Erhan Pişkin","doi":"10.1002/mana.70229","DOIUrl":"https://doi.org/10.1002/mana.70229","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper investigates a class of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>(</mo>\u0000 <mi>x</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$p(x)$</annotation>\u0000 </semantics></math>-Laplacian-viscoelastic wave equations with logarithmic source terms, defined on a bounded domain <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Ω</mi>\u0000 <mo>⊂</mo>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$Omega subset mathbb {R}^{n}$</annotation>\u0000 </semantics></math>. First, we prove the local existence of solutions by using the Faedo–Galerkin method. Next, by combining analytical techniques, including the potential well method and energy estimates, we establish the global existence of solutions. Furthermore, employing the Komornik inequality, we prove the asymptotic stability of these solutions. Finally, through an integration of the potential well framework with concavity arguments, we demonstrate the occurrence of blow-up phenomena under conditions of positive initial energy and derive an upper bound for the blow-up time.</p></div>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 10","pages":"3066-3089"},"PeriodicalIF":1.0,"publicationDate":"2026-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149100061","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":"Boundedness of Multilinear Littlewood–Paley Operators With Convolution Type Kernels on Products of BMO Spaces","authors":"Runzhe Zhang,&nbsp;Hua Wang","doi":"10.1002/mana.70226","DOIUrl":"https://doi.org/10.1002/mana.70226","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, the authors establish the existence and boundedness of multilinear Littlewood–Paley operators on the product of BMO spaces, including the multilinear <span></span><math>\u0000 <semantics>\u0000 <mi>g</mi>\u0000 <annotation>$g$</annotation>\u0000 </semantics></math>-function, multilinear Lusin's area integral and multilinear <span></span><math>\u0000 <semantics>\u0000 <msubsup>\u0000 <mi>g</mi>\u0000 <mi>λ</mi>\u0000 <mo>*</mo>\u0000 </msubsup>\u0000 <annotation>$g^{ast }_{lambda }$</annotation>\u0000 </semantics></math>-function. The authors prove that if the above multilinear operators are finite for a single point, then they are finite almost everywhere. Moreover, it is shown that these multilinear operators are bounded from <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>BMO</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mo>×</mo>\u0000 <mi>⋯</mi>\u0000 <mo>×</mo>\u0000 <mi>BMO</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$mathrm{BMO}(mathbb {R}^n)times cdots times mathrm{BMO}(mathbb {R}^n)$</annotation>\u0000 </semantics></math> into <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>BLO</mi>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$mathrm{BLO}(mathbb {R}^n)$</annotation>\u0000 </semantics></math> (the space of functions with bounded lower oscillation), which is a proper subspace of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>BMO</mi>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$mathrm{BMO}(mathbb {R}^n)$</annotation>\u0000 </semantics></math> (the space of functions with bounded mean oscillation). The corresponding estimates for multilinear Littlewood–Paley operators with non-convolution type kernels are also discussed.</p>\u0000 </div>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 10","pages":"2983-3014"},"PeriodicalIF":1.0,"publicationDate":"2026-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149100341","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":"Interpolation Theorems for Urysohn-Type Nonlinear Operators","authors":"Victor Burenkov,&nbsp;Erlan Nursultanov","doi":"10.1002/mana.70230","DOIUrl":"https://doi.org/10.1002/mana.70230","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we establish interpolation theorems for generalized Morrey-type spaces for a broad class of nonlinear operators, namely, Urysohn-type operators. Using these results, we prove Marcinkiewicz- and Stein–Weiss-type interpolation theorems for such operators.</p></div>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 10","pages":"3090-3106"},"PeriodicalIF":1.0,"publicationDate":"2026-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149100296","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":"Hearing the Serre Invariant of a Compact p-Adic Analytic Manifold","authors":"Patrick Erik Bradley,&nbsp;Ángel Morán Ledezma","doi":"10.1002/mana.70232","DOIUrl":"https://doi.org/10.1002/mana.70232","url":null,"abstract":"&lt;p&gt;Using a previous novel way of defining kernel functions for Laplacian integral operators on a compact &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;annotation&gt;$p$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-adic analytic manifold &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;annotation&gt;$X$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, one such operator &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mi&gt;Δ&lt;/mi&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;annotation&gt;$Delta _0^s$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; with &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$sin mathbb {R}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is applied to hearing the Serre invariant &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;i&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$i(X)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; by showing that a wavelet eigenvalue (with the wavelet having small support) is always congruent to &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;i&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$i(X)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; modulo &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;q&lt;/mi&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$q-1$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, where &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;q&lt;/mi&gt;\u0000 &lt;annotation&gt;$q$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is the cardinality of the residue field &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;annotation&gt;$k$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; attached to a &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;annotation&gt;$p$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-adic number field &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;K&lt;/mi&gt;\u0000 &lt;annotation&gt;$K$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. It is shown how the number of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;annotation&gt;$k$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-rat","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 10","pages":"3126-3138"},"PeriodicalIF":1.0,"publicationDate":"2026-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.70232","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149100060","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":"Kernel Bounds for Parabolic Operators Having First-Order Degeneracy at the Boundary","authors":"L. Negro,&nbsp;C. Spina","doi":"10.1002/mana.70220","DOIUrl":"https://doi.org/10.1002/mana.70220","url":null,"abstract":"<p>We study kernel estimates for parabolic problems governed by singular elliptic operators\u0000\u0000 </p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 10","pages":"2894-2917"},"PeriodicalIF":1.0,"publicationDate":"2026-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.70220","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149100697","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":"Convergence Results for Proximal-Type Algorithm Beyond the Classical Golden-Ratio Constant for Equilibrium Problems","authors":"Renqi Xu,&nbsp;Lateef O. Jolaoso,&nbsp;Yekini Shehu","doi":"10.1002/mana.70202","DOIUrl":"https://doi.org/10.1002/mana.70202","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;The golden-ratio algorithm has recently emerged as an elegant approach for solving variational inequality problems, employing a parameter &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;ϕ&lt;/mi&gt;\u0000 &lt;annotation&gt;$phi$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; traditionally restricted to the interval &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mfrac&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;msqrt&gt;\u0000 &lt;mn&gt;5&lt;/mn&gt;\u0000 &lt;/msqrt&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mfrac&gt;\u0000 &lt;mo&gt;]&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$(1, frac{1+sqrt {5}}{2}]$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. In this work, we prove that the admissible range of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;ϕ&lt;/mi&gt;\u0000 &lt;annotation&gt;$phi$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; can be extended to &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mfenced&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mfrac&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;3&lt;/mn&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;msqrt&gt;\u0000 &lt;mn&gt;33&lt;/mn&gt;\u0000 &lt;/msqrt&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mn&gt;4&lt;/mn&gt;\u0000 &lt;/mfrac&gt;\u0000 &lt;/mfenced&gt;\u0000 &lt;annotation&gt;$left(1,frac{3+sqrt {33}}{4}right)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; within the broader framework of equilibrium problems, a genuine generalization that reveals the classical golden-ratio bound to be a special case rather than an intrinsic limitation. Alongside this parameter-space extension, we introduce a novel self-adaptive step-size strategy that generates step sizes becoming &lt;i&gt;nondecreasing&lt;/i&gt; after finitely many iterations, fundamentally departing from the nonincreasing step sizes required by all existing methods. This new step-size dynamics enables interesting convergence guarantees: We establish weak convergence under pseudo-monotonicity, and under strong pseudo-monotonicity, we prove &lt;i&gt;linear convergence&lt;/i&gt; for &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;ϕ&lt;/mi&gt;\u0000 &lt;annotation&gt;$phi$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; in the classical range and &lt;i&gt;strong convergence&lt;/i&gt; for &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;ϕ&lt;/mi&gt;\u0000 &lt;annotation&gt;$phi$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; in the extended range, results unavailable in previous golden-ratio algorithms. Each iteration requires only a single proximal evaluation, maintaining computational efficiency. The efficacy of the proposed metho","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 10","pages":"2760-2788"},"PeriodicalIF":1.0,"publicationDate":"2026-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149100083","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":"C0-Semigroups of Weighted Composition Operators on Hardy Spaces of Dirichlet Series","authors":"Chengshi Huang,&nbsp;Maofa Wang","doi":"10.1002/mana.70203","DOIUrl":"https://doi.org/10.1002/mana.70203","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we study properties of the infinitesimal generators of <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>C</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <annotation>$C_{0}$</annotation>\u0000 </semantics></math>-semigroups of composition operators on Hardy spaces <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>H</mi>\u0000 <mi>p</mi>\u0000 </msup>\u0000 <annotation>$mathcal {H}^{p}$</annotation>\u0000 </semantics></math> <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mn>1</mn>\u0000 <mo>≤</mo>\u0000 <mi>p</mi>\u0000 <mo>&lt;</mo>\u0000 <mi>∞</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(1 le p&lt;infty)$</annotation>\u0000 </semantics></math> of Dirichlet series. We also characterize the <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>C</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <annotation>$C_{0}$</annotation>\u0000 </semantics></math>-semigroups of weighted composition operators on <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>H</mi>\u0000 <mi>p</mi>\u0000 </msup>\u0000 <annotation>$mathcal {H}^{p}$</annotation>\u0000 </semantics></math> by using abelian intertwiners of multiplication operators. Moreover, we establish a necessary and sufficient condition for embedding a weighted composition operator into a <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>C</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <annotation>$C_{0}$</annotation>\u0000 </semantics></math>-semigroup on <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>H</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <annotation>$mathcal {H}^{2}$</annotation>\u0000 </semantics></math>.</p></div>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 9","pages":"2495-2512"},"PeriodicalIF":1.0,"publicationDate":"2026-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148872156","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":"Dynamics for a Viscoelastic Beam Equation With Past History and Nonlocal Boundary Dissipation","authors":"Linfang Liu,&nbsp;Vando Narciso,&nbsp;Zhijian Yang","doi":"10.1002/mana.70208","DOIUrl":"https://doi.org/10.1002/mana.70208","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;This article aims to study the long-time dynamics of the linear viscoelastic plate equation &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;Δ&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mo&gt;∫&lt;/mo&gt;\u0000 &lt;mi&gt;τ&lt;/mi&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;mi&gt;g&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;Δ&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$ {u_{tt}+Delta ^2 u-int _{tau }^tg(t-s)Delta ^2u(s)ds=0}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; subject to nonlinear and nonlocal boundary conditions. This model, with &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;τ&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$tau =0$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, was first considered by Cavalcanti [&lt;i&gt;Discrete and Continuous Dynamical Systems&lt;/i&gt; 8, no. 3 (2002): 675–695], where results of global existence and uniform decay rates of energy have been established. In this work, by taking &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;τ&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mi&gt;∞&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$tau =-infty$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, and considering the autonomous equivalent problem we prove that the dynamical system &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;S&lt;/mi&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$(mathcal {H},S_t)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; generated by the weak solutions has a compact global attractor &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semant","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 9","pages":"2590-2623"},"PeriodicalIF":1.0,"publicationDate":"2026-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148871876","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}