Journal of Functional Analysis最新文献

{"title":"A Moebius invariant space of H-harmonic functions on the ball","authors":"Petr Blaschke ,&nbsp;Miroslav Engliš ,&nbsp;El-Hassan Youssfi","doi":"10.1016/j.jfa.2025.110857","DOIUrl":"10.1016/j.jfa.2025.110857","url":null,"abstract":"<div><div>It has been an open problem — at least since M. Stoll's book “Harmonic and subharmonic function theory on the hyperbolic ball” (Cambridge University Press, 2016) — whether there exists a Moebius invariant Hilbert space of hyperbolic-harmonic functions on the unit ball of the real <em>n</em>-space, i.e. of functions annihilated by the hyperbolic Laplacian on the ball. We give an answer by describing a Dirichlet-type space of hyperbolic-harmonic functions, as the analytic continuation (in the spirit of Rossi and Vergne) of the corresponding weighted Bergman spaces. Characterizations in terms of derivatives are given, and the associated semi-inner product is shown to be Moebius invariant. We also give a formula for the corresponding reproducing kernel.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 9","pages":"Article 110857"},"PeriodicalIF":1.7,"publicationDate":"2025-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143419654","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}

{"title":"Sharp restricted weak-type estimates for sparse operators","authors":"Irina Holmes Fay ,&nbsp;Guillermo Rey ,&nbsp;Kristina Ana Škreb","doi":"10.1016/j.jfa.2025.110854","DOIUrl":"10.1016/j.jfa.2025.110854","url":null,"abstract":"<div><div>We find the exact Bellman function associated to the level-sets of sparse operators acting on characteristic functions.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 11","pages":"Article 110854"},"PeriodicalIF":1.7,"publicationDate":"2025-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143421999","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}

{"title":"Almost compact embeddings between Orlicz and Lorentz spaces","authors":"Vít Musil ,&nbsp;Luboš Pick ,&nbsp;Jakub Takáč","doi":"10.1016/j.jfa.2025.110859","DOIUrl":"10.1016/j.jfa.2025.110859","url":null,"abstract":"<div><div>We characterize when an Orlicz space <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>A</mi></mrow></msup></math></span> is almost compactly (uniformly absolutely continuously) embedded into a Lorentz space <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi><mo>,</mo><mi>q</mi></mrow></msup></math></span> in terms of a balance condition involving parameters <span><math><mi>p</mi><mo>,</mo><mi>q</mi><mo>∈</mo><mo>[</mo><mn>1</mn><mo>,</mo><mo>∞</mo><mo>]</mo></math></span>, and a Young function <em>A</em>. In the course of the proof, we develop a new method based on an inequality of Young type involving the measure of level sets of a given function.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 11","pages":"Article 110859"},"PeriodicalIF":1.7,"publicationDate":"2025-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143445539","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":"Microscopic derivation of a Schrödinger equation in dimension one with a nonlinear point interaction","authors":"Riccardo Adami ,&nbsp;Jinyeop Lee","doi":"10.1016/j.jfa.2025.110866","DOIUrl":"10.1016/j.jfa.2025.110866","url":null,"abstract":"<div><div>We derive an effective equation for the dynamics of many identical bosons in dimension one in the presence of a tiny impurity. The interaction between every pair of bosons is mediated by the impurity through a positive three-body potential. Assuming a simultaneous mean-field and short-range scaling with the short-range proceeding slower than the mean-field, and choosing an initial fully condensed state, we prove propagation of chaos and obtain an effective one-particle Schrödinger equation with a defocusing nonlinearity concentrated at a point. More precisely, we prove convergence of one-particle density operators in the trace-class topology and estimate the fluctuations as superexponential. This is the first derivation of the so-called nonlinear delta model, widely investigated in the last decades, as a phenomenological model for several physical phenomena.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 10","pages":"Article 110866"},"PeriodicalIF":1.7,"publicationDate":"2025-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143403636","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}

{"title":"Local regularity of the Bergman projection on a class of pseudoconvex domains of finite type","authors":"T.V. Khanh ,&nbsp;A. Raich","doi":"10.1016/j.jfa.2025.110855","DOIUrl":"10.1016/j.jfa.2025.110855","url":null,"abstract":"<div><div>The purpose of this paper is to prove that if a pseudoconvex domains <span><math><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> satisfies Bell-Ligocka's Condition R and admits a “good” dilation, then the Bergman projection has local <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>-Sobolev and Hölder estimates. The good dilation structure is phrased in terms of uniform <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> pseudolocal estimates for the Bergman projection on a family of anisotropic scalings. We conclude the paper by showing that <em>h</em>-extendible domains satisfy our hypotheses.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 10","pages":"Article 110855"},"PeriodicalIF":1.7,"publicationDate":"2025-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143429911","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":"Generalized de Branges-Rovnyak spaces","authors":"Alexandru Aleman,&nbsp;Frej Dahlin","doi":"10.1016/j.jfa.2025.110860","DOIUrl":"10.1016/j.jfa.2025.110860","url":null,"abstract":"<div><div>Given the reproducing kernel <em>k</em> of the Hilbert space <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>k</mi></mrow></msub></math></span> we study spaces <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>(</mo><mi>b</mi><mo>)</mo></math></span> whose reproducing kernel has the form <span><math><mi>k</mi><mo>(</mo><mn>1</mn><mo>−</mo><mi>b</mi><msup><mrow><mi>b</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>)</mo></math></span>, where <em>b</em> is a row-contraction on <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>k</mi></mrow></msub></math></span>. In terms of reproducing kernels this is the most far-reaching generalization of the classical de Branges-Rovnyaks spaces, as well as their very recent generalization to several variables. This includes the so called sub-Bergman spaces <span><span>[31]</span></span> in one or several variables. We study some general properties of <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>(</mo><mi>b</mi><mo>)</mo></math></span> e.g. when the inclusion map into <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>k</mi></mrow></msub></math></span> is compact. Our main result provides a model for <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>(</mo><mi>b</mi><mo>)</mo></math></span> reminiscent of the Sz.-Nagy-Foiaş model for contractions (see also <span><span>[7]</span></span>). As an application we obtain sufficient conditions for the containment and density of the linear span of <span><math><mo>{</mo><msub><mrow><mi>k</mi></mrow><mrow><mi>w</mi></mrow></msub><mo>:</mo><mi>w</mi><mo>∈</mo><mi>X</mi><mo>}</mo></math></span> in <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>(</mo><mi>b</mi><mo>)</mo></math></span>. In the standard cases this reduces to containment and density of polynomials. These methods resolve a very recent conjecture <span><span>[13]</span></span> regarding polynomial approximation in spaces with kernel <span><math><mfrac><mrow><msup><mrow><mo>(</mo><mn>1</mn><mo>−</mo><mi>b</mi><mo>(</mo><mi>z</mi><mo>)</mo><mi>b</mi><msup><mrow><mo>(</mo><mi>w</mi><mo>)</mo></mrow><mrow><mo>⁎</mo></mrow></msup><mo>)</mo></mrow><mrow><mi>m</mi></mrow></msup></mrow><mrow><msup><mrow><mo>(</mo><mn>1</mn><mo>−</mo><mi>z</mi><mover><mrow><mi>w</mi></mrow><mo>‾</mo></mover><mo>)</mo></mrow><mrow><mi>β</mi></mrow></msup></mrow></mfrac><mo>,</mo><mn>1</mn><mo>≤</mo><mi>m</mi><mo>&lt;</mo><mi>β</mi><mo>,</mo><mi>m</mi><mo>∈</mo><mi>N</mi></math></span>.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 11","pages":"Article 110860"},"PeriodicalIF":1.7,"publicationDate":"2025-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143437217","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}

{"title":"A unique Cartan subalgebra result for Bernoulli actions of weakly amenable groups","authors":"Changying Ding","doi":"10.1016/j.jfa.2025.110852","DOIUrl":"10.1016/j.jfa.2025.110852","url":null,"abstract":"<div><div>We show that if <span><math><mi>Γ</mi><mspace></mspace><mo>↷</mo><mspace></mspace><mo>(</mo><msup><mrow><mi>X</mi></mrow><mrow><mi>Γ</mi></mrow></msup><mo>,</mo><msup><mrow><mi>μ</mi></mrow><mrow><mi>Γ</mi></mrow></msup><mo>)</mo></math></span> is a Bernoulli action of an i.c.c. nonamenable group Γ which is weakly amenable with Cowling-Haagerup constant 1, and <span><math><mi>Λ</mi><mspace></mspace><mo>↷</mo><mspace></mspace><mo>(</mo><mi>Y</mi><mo>,</mo><mi>ν</mi><mo>)</mo></math></span> is a free ergodic p.m.p. algebraic action of a group Λ, then the isomorphism <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>(</mo><msup><mrow><mi>X</mi></mrow><mrow><mi>Γ</mi></mrow></msup><mo>)</mo><mo>⋊</mo><mi>Γ</mi><mo>≅</mo><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>(</mo><mi>Y</mi><mo>)</mo><mo>⋊</mo><mi>Λ</mi></math></span> implies that <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>(</mo><msup><mrow><mi>X</mi></mrow><mrow><mi>Γ</mi></mrow></msup><mo>)</mo></math></span> and <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>(</mo><mi>Y</mi><mo>)</mo></math></span> are unitarily conjugate. This is obtained by showing a new rigidity result of non properly proximal groups and combining it with a rigidity result of properly proximal groups from <span><span>[1]</span></span>.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 10","pages":"Article 110852"},"PeriodicalIF":1.7,"publicationDate":"2025-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143403637","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":"On pointwise convergence of cone multipliers","authors":"Peng Chen ,&nbsp;Danqing He ,&nbsp;Xiaochun Li ,&nbsp;Lixin Yan","doi":"10.1016/j.jfa.2025.110853","DOIUrl":"10.1016/j.jfa.2025.110853","url":null,"abstract":"<div><div>We study the pointwise convergence of the cone multipliers<span><span><span><math><msup><mrow><mover><mrow><mi>T</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><mi>λ</mi></mrow></msup><mo>(</mo><mi>f</mi><mo>)</mo><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><munder><mo>∫</mo><mrow><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></mrow></munder><msubsup><mrow><mo>(</mo><mn>1</mn><mo>−</mo><mfrac><mrow><msup><mrow><mi>t</mi></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup><mo>|</mo><msup><mrow><mi>ξ</mi></mrow><mrow><mo>′</mo></mrow></msup><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><msubsup><mrow><mi>ξ</mi></mrow><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msubsup></mrow></mfrac><mo>)</mo></mrow><mrow><mo>+</mo></mrow><mrow><mi>λ</mi></mrow></msubsup><mover><mrow><mi>f</mi></mrow><mrow><mo>ˆ</mo></mrow></mover><mo>(</mo><mi>ξ</mi><mo>)</mo><msup><mrow><mi>e</mi></mrow><mrow><mn>2</mn><mi>π</mi><mi>i</mi><mi>x</mi><mo>⋅</mo><mi>ξ</mi></mrow></msup><mi>d</mi><mi>ξ</mi><mo>.</mo></math></span></span></span> For <span><math><mi>p</mi><mo>≥</mo><mn>2</mn></math></span>, and <span><math><mi>λ</mi><mo>&gt;</mo><mi>max</mi><mo>⁡</mo><mo>{</mo><mi>n</mi><mo>|</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>p</mi></mrow></mfrac><mo>−</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>|</mo><mo>−</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>,</mo><mn>0</mn><mo>}</mo></math></span>, we prove the pointwise convergence of cone multipliers, i.e.<span><span><span><math><munder><mi>lim</mi><mrow><mi>t</mi><mo>→</mo><mo>∞</mo></mrow></munder><mo>⁡</mo><msubsup><mrow><mover><mrow><mi>T</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><mi>t</mi></mrow><mrow><mi>λ</mi></mrow></msubsup><mo>(</mo><mi>f</mi><mo>)</mo><mo>→</mo><mi>f</mi><mtext> a.e.</mtext><mo>,</mo></math></span></span></span> where <span><math><mi>f</mi><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></math></span> satisfies <span><math><mrow><mtext>supp</mtext><mspace></mspace></mrow><mover><mrow><mi>f</mi></mrow><mrow><mo>ˆ</mo></mrow></mover><mo>⊂</mo><mo>{</mo><mi>ξ</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>:</mo><mspace></mspace><mn>1</mn><mo>&lt;</mo><mo>|</mo><msub><mrow><mi>ξ</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>|</mo><mo>&lt;</mo><mn>2</mn><mo>}</mo></math></span>. Our main tools are weighted estimates for maximal cone operators, which are consequences of trace inequalities for cones.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 9","pages":"Article 110853"},"PeriodicalIF":1.7,"publicationDate":"2025-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143419549","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":"Multiple closed geodesics on Finsler 3-dimensional sphere","authors":"Huagui Duan ,&nbsp;Zihao Qi","doi":"10.1016/j.jfa.2025.110863","DOIUrl":"10.1016/j.jfa.2025.110863","url":null,"abstract":"<div><div>In 1973, Katok constructed a non-degenerate (also called bumpy) Finsler metric on <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> with exactly four prime closed geodesics. Then Anosov conjectured that four should be the optimal lower bound of the number of prime closed geodesics on every Finsler <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>. In this paper, we prove this conjecture for a bumpy Finsler <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> if the Morse index of any prime closed geodesic is nonzero.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 10","pages":"Article 110863"},"PeriodicalIF":1.7,"publicationDate":"2025-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143421904","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 better bound on blow-up rate for the superconformal semilinear wave equation","authors":"Mohamed Ali Hamza ,&nbsp;Hatem Zaag","doi":"10.1016/j.jfa.2025.110862","DOIUrl":"10.1016/j.jfa.2025.110862","url":null,"abstract":"<div><div>We consider the semilinear wave equation in higher dimensions with superconformal power nonlinearity. The purpose of this paper is to give a new upper bound on the blow-up rate in some space-time integral, showing a <span><math><mo>|</mo><mi>log</mi><mo>⁡</mo><mo>(</mo><mi>T</mi><mo>−</mo><mi>t</mi><mo>)</mo><msup><mrow><mo>|</mo></mrow><mrow><mi>q</mi></mrow></msup></math></span> improvement in comparison with previous results obtained in <span><span>[14]</span></span>, <span><span>[16]</span></span>.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 11","pages":"Article 110862"},"PeriodicalIF":1.7,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143430122","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}