Pub Date : 2025-02-10DOI: 10.1016/j.jfa.2025.110865
Kyeongsu Choi , Liming Sun
We classify closed convex ancient α-curve shortening flows for sub-affine-critical powers . In addition, we show that closed convex smooth finite entropy ancient α-curve shortening flows with 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 with , the round circle shrinker has non-trivial Jacobi fields, but the ancient flows asymptotic to shrinking circles do not evolve along the Jacobi fields.
{"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}
Pub Date : 2025-02-10DOI: 10.1016/j.jfa.2025.110856
C. Bellavita , V. Daskalogiannis , S. Miihkinen , D. Norrbo , G. Stylogiannis , J. Virtanen
In this article, we study the generalized Hilbert matrix operator acting on the Bergman spaces of the unit disc for . In particular, we characterize the measures μ for which the operator is bounded, determine the exact value of the norm for , and provide norm estimates for the other values of p. Additionally, we observe an unexpected behavior in the case . Finally, we characterize the measures μ for which is compact by calculating its exact essential norm.
{"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}
Pub Date : 2025-02-10DOI: 10.1016/j.jfa.2025.110864
Pablo López-Rivera , Yair Shenfeld
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.
{"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}
Pub Date : 2025-02-10DOI: 10.1016/j.jfa.2025.110858
Jiaxi Huang , Ning Jiang , Lifeng Zhao
This article is devoted to the simplified Ericksen-Leslie's hyperbolic system for incompressible liquid crystal model in two spatial dimensions, which is a nonlinear coupling of incompressible Navier-Stokes equations with wave map to circle . The structure of second-order material derivative is exploited in order to close the energy estimates. We established the almost global well-posedness for small and smooth initial data near the constant equilibrium. Our proof relies on the idea of vector-field method and ghost weight method.
{"title":"Almost global well-posedness of Ericksen-Leslie's hyperbolic liquid crystal model for small data in two dimensions","authors":"Jiaxi Huang , Ning Jiang , Lifeng Zhao","doi":"10.1016/j.jfa.2025.110858","DOIUrl":"10.1016/j.jfa.2025.110858","url":null,"abstract":"<div><div>This article is devoted to the simplified Ericksen-Leslie's hyperbolic system for incompressible liquid crystal model in two spatial dimensions, which is a nonlinear coupling of incompressible Navier-Stokes equations with wave map to circle <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>. The structure of second-order material derivative is exploited in order to close the energy estimates. We established the almost global well-posedness for small and smooth initial data near the constant equilibrium. Our proof relies on the idea of vector-field method and ghost weight method.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 10","pages":"Article 110858"},"PeriodicalIF":1.7,"publicationDate":"2025-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143429912","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}
Pub Date : 2025-02-10DOI: 10.1016/j.jfa.2025.110857
Petr Blaschke , Miroslav Engliš , El-Hassan Youssfi
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 n-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.
{"title":"A Moebius invariant space of H-harmonic functions on the ball","authors":"Petr Blaschke , Miroslav Engliš , 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}
Pub Date : 2025-02-10DOI: 10.1016/j.jfa.2025.110854
Irina Holmes Fay , Guillermo Rey , Kristina Ana Škreb
We find the exact Bellman function associated to the level-sets of sparse operators acting on characteristic functions.
{"title":"Sharp restricted weak-type estimates for sparse operators","authors":"Irina Holmes Fay , Guillermo Rey , 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}
Pub Date : 2025-02-10DOI: 10.1016/j.jfa.2025.110859
Vít Musil , Luboš Pick , Jakub Takáč
We characterize when an Orlicz space is almost compactly (uniformly absolutely continuously) embedded into a Lorentz space in terms of a balance condition involving parameters , and a Young function A. 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.
{"title":"Almost compact embeddings between Orlicz and Lorentz spaces","authors":"Vít Musil , Luboš Pick , 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}
Pub Date : 2025-02-10DOI: 10.1016/j.jfa.2025.110866
Riccardo Adami , Jinyeop Lee
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.
{"title":"Microscopic derivation of a Schrödinger equation in dimension one with a nonlinear point interaction","authors":"Riccardo Adami , 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}
Pub Date : 2025-02-10DOI: 10.1016/j.jfa.2025.110855
T.V. Khanh , A. Raich
The purpose of this paper is to prove that if a pseudoconvex domains satisfies Bell-Ligocka's Condition R and admits a “good” dilation, then the Bergman projection has local -Sobolev and Hölder estimates. The good dilation structure is phrased in terms of uniform pseudolocal estimates for the Bergman projection on a family of anisotropic scalings. We conclude the paper by showing that h-extendible domains satisfy our hypotheses.
{"title":"Local regularity of the Bergman projection on a class of pseudoconvex domains of finite type","authors":"T.V. Khanh , 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}
Pub Date : 2025-02-10DOI: 10.1016/j.jfa.2025.110852
Changying Ding
We show that if is a Bernoulli action of an i.c.c. nonamenable group Γ which is weakly amenable with Cowling-Haagerup constant 1, and is a free ergodic p.m.p. algebraic action of a group Λ, then the isomorphism implies that and 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 [1].
{"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}
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