{"title":"Upper bounds for solutions of Leibenson's equation on Riemannian manifolds","authors":"Alexander Grigor'yan, Philipp Sürig","doi":"10.1016/j.jfa.2025.110878","DOIUrl":"10.1016/j.jfa.2025.110878","url":null,"abstract":"<div><div>We consider on Riemannian manifolds the Leibenson equation<span><span><span><math><msub><mrow><mo>∂</mo></mrow><mrow><mi>t</mi></mrow></msub><mi>u</mi><mo>=</mo><msub><mrow><mi>Δ</mi></mrow><mrow><mi>p</mi></mrow></msub><msup><mrow><mi>u</mi></mrow><mrow><mi>q</mi></mrow></msup></math></span></span></span>that is also known as a doubly nonlinear evolution equation. We prove upper estimates of weak subsolutions to this equation on Riemannian manifolds with non-negative Ricci curvature in the case when <em>p</em> and <em>q</em> satisfy the conditions<span><span><span><math><mn>1</mn><mo><</mo><mi>p</mi><mo><</mo><mn>2</mn><mspace></mspace><mtext>and</mtext><mspace></mspace><mn>1</mn><mo>≤</mo><mi>q</mi><mo><</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>p</mi><mo>−</mo><mn>1</mn></mrow></mfrac><mo>.</mo></math></span></span></span> We show that these estimates are optimal in terms of long time behavior and near-optimal in terms of long distance behavior.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 10","pages":"Article 110878"},"PeriodicalIF":1.7,"publicationDate":"2025-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143445069","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Guozheng Cheng , Xiang Fang , Chao Liu , Yufeng Lu
{"title":"Littlewood-type theorems for random Dirichlet multipliers","authors":"Guozheng Cheng , Xiang Fang , Chao Liu , Yufeng Lu","doi":"10.1016/j.jfa.2025.110851","DOIUrl":"10.1016/j.jfa.2025.110851","url":null,"abstract":"<div><div>In this paper we present a systematic study of random Dirichlet functions. In 1993, Cochran-Shapiro-Ullrich proved the following elegant result on random Dirichlet multipliers <span><span>[21]</span></span>: For any <span><math><mi>f</mi><mo>(</mo><mi>z</mi><mo>)</mo><mo>=</mo><msubsup><mrow><mo>∑</mo></mrow><mrow><mi>n</mi><mo>=</mo><mn>0</mn></mrow><mrow><mo>∞</mo></mrow></msubsup><msub><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msub><msup><mrow><mi>z</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>∈</mo><mi>D</mi></math></span>, the Dirichlet space over the unit disk, almost all of its randomizations<span><span><span><math><mo>(</mo><mi>R</mi><mi>f</mi><mo>)</mo><mo>(</mo><mi>z</mi><mo>)</mo><mo>=</mo><munderover><mo>∑</mo><mrow><mi>n</mi><mo>=</mo><mn>0</mn></mrow><mrow><mo>∞</mo></mrow></munderover><mo>±</mo><msub><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msub><msup><mrow><mi>z</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span></span></span> are multipliers of <span><math><mi>D</mi></math></span>. The purpose of this paper is to exploit this result and to extend it in three directions, inspired by the 1930 theorem of Littlewood on random Hardy functions:<ul><li><span>(A)</span><span><div>We introduce a symbol space <span><math><msub><mrow><mi>M</mi></mrow><mrow><mo>⋆</mo></mrow></msub></math></span> for random multipliers on <span><math><mi>D</mi></math></span> and reformulate (and strengthen) the problem as the characterization of <span><math><msub><mrow><mi>M</mi></mrow><mrow><mo>⋆</mo></mrow></msub></math></span>. We then characterize <span><math><msub><mrow><mo>(</mo><msubsup><mrow><mi>M</mi></mrow><mrow><mi>α</mi></mrow><mrow><mi>p</mi></mrow></msubsup><mo>)</mo></mrow><mrow><mo>⋆</mo></mrow></msub></math></span> for all <span><math><mi>p</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo><mo>,</mo><mi>α</mi><mo>∈</mo><mo>(</mo><mo>−</mo><mn>1</mn><mo>,</mo><mo>∞</mo><mo>)</mo></math></span> when <span><math><mi>α</mi><mo>≠</mo><mi>p</mi><mo>−</mo><mn>1</mn></math></span> (<span><span>Theorem 55</span></span>). The case <span><math><mi>p</mi><mo>=</mo><mn>2</mn><mo>,</mo><mi>α</mi><mo>=</mo><mn>0</mn></math></span> recovers the 1993 result.</div></span></li><li><span>(B)</span><span><div>We obtain a two-parameter version by formulating and solving a Littlewood-type problem for all <span><math><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo><mo>∈</mo><msup><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></math></span> (<span><span>Theorem 69</span></span>). The case <span><math><mi>p</mi><mo>=</mo><mi>q</mi><mo>=</mo><mn>2</mn></math></span> recovers the 1993 result.</div></span></li><li><span>(C)</span><span><div>We consider <span><math><msubsup><mrow><mi>D</mi></mrow><mrow><mi>p</mi><mo>−</mo><mn>1</mn></mrow><mrow><mi>p</mi></mrow></msubsup></math></span> and <span><math><msubsup><mrow><mi>D</mi></mrow><mrow><mi>p</mi><mo>−</mo><mn>2</mn></mrow><mrow><m","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 12","pages":"Article 110851"},"PeriodicalIF":1.7,"publicationDate":"2025-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143509749","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The generalized Riemann zeta heat flow","authors":"Víctor Castillo , Claudio Muñoz , Felipe Poblete , Vicente Salinas","doi":"10.1016/j.jfa.2025.110879","DOIUrl":"10.1016/j.jfa.2025.110879","url":null,"abstract":"<div><div>We consider the PDE flow associated to Riemann zeta and general Dirichlet <em>L</em>-functions. These are models characterized by nonlinearities appearing in classical number theory problems, and generalizing the classical holomorphic Riemann flow studied by Broughan and Barnett. Each zero of a Dirichlet <em>L</em>-function is an exact solution of the model. In this paper, we first show local existence of bounded continuous solutions in the Duhamel sense to any Dirichlet <em>L</em>-function flow with initial condition far from the pole (as long as this exists). In a second result, we prove global existence in the case of nonlinearities of the form Dirichlet <em>L</em>-functions and data initially on the right of a possible pole at <span><math><mi>s</mi><mo>=</mo><mn>1</mn></math></span>. Additional global well-posedness and convergence results are proved in the case of the defocussing Riemann zeta nonlinearity and initial data located on the real line and close to the trivial zeros of the zeta. The asymptotic stability of any stable zero is also proved. Finally, in the Riemann zeta case, we consider the “focusing” model, and prove blow-up of real-valued solutions near the pole <span><math><mi>s</mi><mo>=</mo><mn>1</mn></math></span>.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 10","pages":"Article 110879"},"PeriodicalIF":1.7,"publicationDate":"2025-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143429913","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Morse theory for the Allen-Cahn functional","authors":"Jingwen Chen , Pedro Gaspar","doi":"10.1016/j.jfa.2025.110876","DOIUrl":"10.1016/j.jfa.2025.110876","url":null,"abstract":"<div><div>In this article, we use Morse-theoretic techniques to construct connections between low energy critical submanifolds of the Allen-Cahn energy functional in the 3-sphere via the negative gradient flow.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 9","pages":"Article 110876"},"PeriodicalIF":1.7,"publicationDate":"2025-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143419655","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A representation-theoretic approach to Toeplitz quantization on flag manifolds","authors":"Matthew Dawson, Yessica Hernández-Eliseo","doi":"10.1016/j.jfa.2025.110877","DOIUrl":"10.1016/j.jfa.2025.110877","url":null,"abstract":"<div><div>In this paper, we study Toeplitz operators on generalized flag manifolds of compact Lie groups using a representation-theoretic point of view. We prove several basic properties of these Toeplitz operators, including an abstract formula for their matrix coefficients in terms of the decomposition of certain tensor product representations. We also show how to identify large commuting families of Toeplitz operators based on invariance of their symbols under certain subgroups. Finally, we realize the Berezin transform as a convolution with certain functions that form an approximate identity on the generalized flag manifold, which allows us to prove a Szegő Limit Theorem using certain results due to Hirschman, Liang, and Wilson.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 9","pages":"Article 110877"},"PeriodicalIF":1.7,"publicationDate":"2025-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143403065","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Schatten class little Hankel operators on Bergman spaces in bounded symmetric domains","authors":"Wenwan Yang, Cheng Yuan","doi":"10.1016/j.jfa.2025.110875","DOIUrl":"10.1016/j.jfa.2025.110875","url":null,"abstract":"<div><div>Suppose <span><math><mi>α</mi><mo>></mo><mo>−</mo><mn>1</mn></math></span>, <span><math><mfrac><mrow><mi>a</mi><mo>(</mo><mi>r</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow><mrow><mi>N</mi><mo>+</mo><mi>α</mi></mrow></mfrac><mo><</mo><mi>p</mi><mo><</mo><mn>1</mn></math></span> and <em>f</em> belongs to the Bergman space <span><math><msubsup><mrow><mi>A</mi></mrow><mrow><mi>α</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mo>(</mo><mi>Ω</mi><mo>)</mo></math></span> in the bounded symmetric domain Ω of <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>. We prove that the little Hankel operator <span><math><msubsup><mrow><mi>h</mi></mrow><mrow><mover><mrow><mi>f</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>α</mi></mrow></msubsup></math></span> acting on <span><math><msubsup><mrow><mi>A</mi></mrow><mrow><mi>α</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mo>(</mo><mi>Ω</mi><mo>)</mo></math></span> is in the Schatten <em>p</em>-class if and only if <em>f</em> is in the Besov space <span><math><msub><mrow><mi>B</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>(</mo><mi>Ω</mi><mo>)</mo></math></span>.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 10","pages":"Article 110875"},"PeriodicalIF":1.7,"publicationDate":"2025-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143403638","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Caffarelli-Kohn-Nirenberg-type inequalities related to weighted p-Laplace equations","authors":"Shengbing Deng, Xingliang Tian","doi":"10.1016/j.jfa.2025.110867","DOIUrl":"10.1016/j.jfa.2025.110867","url":null,"abstract":"<div><div>In this paper, we consider the Caffarelli-Kohn-Nirenberg-type inequality in radial space which admits wider region of parameters than in general space. Firstly, we give the classification of solutions to a linearized problem related to its extremal functions. Then as an application, we investigate the gradient type remainder term of Caffarelli-Kohn-Nirenberg-type inequality by using spectral estimate combined with a compactness argument which extends the work of Figalli and Zhang (2022) <span><span>[20]</span></span> at least for radial case.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 9","pages":"Article 110867"},"PeriodicalIF":1.7,"publicationDate":"2025-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143419573","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Classification of ancient flows by sub-affine-critical powers of curvature in R2","authors":"Kyeongsu Choi , Liming Sun","doi":"10.1016/j.jfa.2025.110865","DOIUrl":"10.1016/j.jfa.2025.110865","url":null,"abstract":"<div><div>We classify closed convex ancient <em>α</em>-curve shortening flows for sub-affine-critical powers <span><math><mi>α</mi><mo>≤</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac></math></span>. In addition, we show that closed convex smooth finite entropy ancient <em>α</em>-curve shortening flows with <span><math><mi>α</mi><mo>></mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac></math></span> are shrinking circles. After rescaling, the ancient flows satisfying the above conditions converge exponentially fast to smooth closed convex shrinkers as the time goes to negative infinity. In particular, when <span><math><mi>α</mi><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><msup><mrow><mi>k</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>−</mo><mn>1</mn></mrow></mfrac></math></span> with <span><math><mn>3</mn><mo>≤</mo><mi>k</mi><mo>∈</mo><mi>N</mi></math></span>, the round circle shrinker has non-trivial Jacobi fields, but the ancient flows asymptotic to shrinking circles do not evolve along the Jacobi fields.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 9","pages":"Article 110865"},"PeriodicalIF":1.7,"publicationDate":"2025-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143419574","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
C. Bellavita , V. Daskalogiannis , S. Miihkinen , D. Norrbo , G. Stylogiannis , J. Virtanen
{"title":"Generalized Hilbert matrix operators acting on Bergman spaces","authors":"C. Bellavita , V. Daskalogiannis , S. Miihkinen , D. Norrbo , G. Stylogiannis , J. Virtanen","doi":"10.1016/j.jfa.2025.110856","DOIUrl":"10.1016/j.jfa.2025.110856","url":null,"abstract":"<div><div>In this article, we study the generalized Hilbert matrix operator <span><math><msub><mrow><mi>Γ</mi></mrow><mrow><mi>μ</mi></mrow></msub></math></span> acting on the Bergman spaces <span><math><msup><mrow><mi>A</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> of the unit disc for <span><math><mn>1</mn><mo>≤</mo><mi>p</mi><mo><</mo><mo>∞</mo></math></span>. In particular, we characterize the measures <em>μ</em> for which the operator <span><math><msub><mrow><mi>Γ</mi></mrow><mrow><mi>μ</mi></mrow></msub></math></span> is bounded, determine the exact value of the norm for <span><math><mi>p</mi><mo>≥</mo><mn>4</mn></math></span>, and provide norm estimates for the other values of <em>p</em>. Additionally, we observe an unexpected behavior in the case <span><math><mi>p</mi><mo>=</mo><mn>2</mn></math></span>. Finally, we characterize the measures <em>μ</em> for which <span><math><msub><mrow><mi>Γ</mi></mrow><mrow><mi>μ</mi></mrow></msub></math></span> is compact by calculating its exact essential norm.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 9","pages":"Article 110856"},"PeriodicalIF":1.7,"publicationDate":"2025-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143419575","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Poisson transport map","authors":"Pablo López-Rivera , Yair Shenfeld","doi":"10.1016/j.jfa.2025.110864","DOIUrl":"10.1016/j.jfa.2025.110864","url":null,"abstract":"<div><div>We construct a transport map from Poisson point processes onto ultra-log-concave measures over the natural numbers, and show that this map is a contraction. Our approach overcomes the known obstacles to transferring functional inequalities using transport maps in discrete settings, and allows us to deduce a number of functional inequalities for ultra-log-concave measures. In particular, we provide the currently best known constant in modified logarithmic Sobolev inequalities for ultra-log-concave measures.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 10","pages":"Article 110864"},"PeriodicalIF":1.7,"publicationDate":"2025-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143421905","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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