Pub Date : 2026-02-15Epub Date: 2025-11-04DOI: 10.1016/j.jfa.2025.111262
Emanuele Caputo , Augusto Gerolin , Nataliia Monina , Lorenzo Portinale
In this manuscript, we study the (finite-dimensional) static formulation of quantum optimal transport problems with general convex regularization and its unbalanced relaxation. In both cases, we show a duality result, characterizations of minimizers (for the primal) and maximizers (for the dual). An important tool we define is a non-commutative version of the classical -transforms associated with a general convex regularization, which we employ to prove the convergence of the associated Sinkhorn iterations. Finally, we show the convergence of the unbalanced transport problems towards the constrained one, as well as the convergence of transforms, as the marginal penalization parameters go to +∞.
{"title":"Quantum optimal transport with convex regularization","authors":"Emanuele Caputo , Augusto Gerolin , Nataliia Monina , Lorenzo Portinale","doi":"10.1016/j.jfa.2025.111262","DOIUrl":"10.1016/j.jfa.2025.111262","url":null,"abstract":"<div><div>In this manuscript, we study the (finite-dimensional) static formulation of quantum optimal transport problems with general convex regularization and its unbalanced relaxation. In both cases, we show a duality result, characterizations of minimizers (for the primal) and maximizers (for the dual). An important tool we define is a non-commutative version of the classical <span><math><mo>(</mo><mi>c</mi><mo>,</mo><mi>ψ</mi><mo>,</mo><mi>ε</mi><mo>)</mo></math></span>-transforms associated with a general convex regularization, which we employ to prove the convergence of the associated Sinkhorn iterations. Finally, we show the convergence of the unbalanced transport problems towards the constrained one, as well as the convergence of transforms, as the marginal penalization parameters go to +∞.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 4","pages":"Article 111262"},"PeriodicalIF":1.6,"publicationDate":"2026-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145518716","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 : 2026-02-15Epub Date: 2025-11-04DOI: 10.1016/j.jfa.2025.111264
Ken Dykema, Junchen Zhao
For a self-symmetric tracial von Neumann algebra A, we study rescalings of for and and use them to obtain an interpolation for all real numbers and . We get formulas for their free products, and free products with finite-dimensional or hyperfinite von Neumann algebras. In particular, for any such A, we can compute compressions for , and the Murray-von Neumann fundamental group of . When A is also non-separable and abelian, this answers two questions in Section 4.3 of [4].
对于自对称跟踪von Neumann代数a，我们研究了n∈n，r∈(1,∞)下a * n * LFr的重标化，并利用它们得到了对所有实数s>；0和1 - s<；r≤∞的插值f，r(a)。我们得到它们的自由积的公式，以及有限维或超有限冯·诺伊曼代数的自由积。特别地，对于任何这样的A，我们可以计算0<；t<；1的压缩（A n）t，以及A∞的Murray-von Neumann基本群。当A也是不可分的且是阿贝尔的，这回答了[4]第4.3节中的两个问题。
{"title":"Free products and rescalings involving non-separable abelian von Neumann algebras","authors":"Ken Dykema, Junchen Zhao","doi":"10.1016/j.jfa.2025.111264","DOIUrl":"10.1016/j.jfa.2025.111264","url":null,"abstract":"<div><div>For a self-symmetric tracial von Neumann algebra <em>A</em>, we study rescalings of <span><math><msup><mrow><mi>A</mi></mrow><mrow><mo>⁎</mo><mi>n</mi></mrow></msup><mo>⁎</mo><mi>L</mi><msub><mrow><mi>F</mi></mrow><mrow><mi>r</mi></mrow></msub></math></span> for <span><math><mi>n</mi><mo>∈</mo><mi>N</mi></math></span> and <span><math><mi>r</mi><mo>∈</mo><mo>(</mo><mn>1</mn><mo>,</mo><mo>∞</mo><mo>]</mo></math></span> and use them to obtain an interpolation <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>s</mi><mo>,</mo><mi>r</mi></mrow></msub><mo>(</mo><mi>A</mi><mo>)</mo></math></span> for all real numbers <span><math><mi>s</mi><mo>></mo><mn>0</mn></math></span> and <span><math><mn>1</mn><mo>−</mo><mi>s</mi><mo><</mo><mi>r</mi><mo>≤</mo><mo>∞</mo></math></span>. We get formulas for their free products, and free products with finite-dimensional or hyperfinite von Neumann algebras. In particular, for any such <em>A</em>, we can compute compressions <span><math><msup><mrow><mo>(</mo><msup><mrow><mi>A</mi></mrow><mrow><mo>⁎</mo><mi>n</mi></mrow></msup><mo>)</mo></mrow><mrow><mi>t</mi></mrow></msup></math></span> for <span><math><mn>0</mn><mo><</mo><mi>t</mi><mo><</mo><mn>1</mn></math></span>, and the Murray-von Neumann fundamental group of <span><math><msup><mrow><mi>A</mi></mrow><mrow><mo>⁎</mo><mo>∞</mo></mrow></msup></math></span>. When <em>A</em> is also non-separable and abelian, this answers two questions in Section 4.3 of <span><span>[4]</span></span>.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 4","pages":"Article 111264"},"PeriodicalIF":1.6,"publicationDate":"2026-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145464989","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 : 2026-02-15Epub Date: 2025-11-04DOI: 10.1016/j.jfa.2025.111252
Jie Wu
In this paper, we establish a broad class of new sharp Alexandrov-Fenchel inequalities involving general convex weight functions for static convex hypersurfaces in hyperbolic space. Additionally, we derive new weighted Minkowski-type inequalities for static convex hypersurfaces in hyperbolic space and for convex hypersurfaces in the sphere . The tools we shall use are the locally constrained inverse curvature flows in hyperbolic space and in the sphere.
{"title":"New weighted Alexandrov-Fenchel type inequalities and Minkowski inequalities in space forms","authors":"Jie Wu","doi":"10.1016/j.jfa.2025.111252","DOIUrl":"10.1016/j.jfa.2025.111252","url":null,"abstract":"<div><div>In this paper, we establish a broad class of new sharp Alexandrov-Fenchel inequalities involving general convex weight functions for static convex hypersurfaces in hyperbolic space. Additionally, we derive new weighted Minkowski-type inequalities for static convex hypersurfaces in hyperbolic space <span><math><msup><mrow><mi>H</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> and for convex hypersurfaces in the sphere <span><math><msup><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>. The tools we shall use are the locally constrained inverse curvature flows in hyperbolic space and in the sphere.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 4","pages":"Article 111252"},"PeriodicalIF":1.6,"publicationDate":"2026-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145464991","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 : 2026-02-15Epub Date: 2025-11-04DOI: 10.1016/j.jfa.2025.111260
Sung-Soo Byun , Seongjae Park
We consider the n eigenvalues of the complex and symplectic induced spherical ensembles, which can be realised as two-dimensional determinantal and Pfaffian Coulomb gases on the Riemann sphere under the insertion of point charges. For both cases, we show that the probability that there are no eigenvalues in a spherical cap around a pole has an asymptotic behaviour as of the form and we determine the coefficients explicitly. Our results provide the second example of precise (up to and including the constant term) large gap asymptotic behaviours for a two-dimensional point process, following a recent breakthrough by Charlier.
{"title":"Large gap probabilities of complex and symplectic spherical ensembles with point charges","authors":"Sung-Soo Byun , Seongjae Park","doi":"10.1016/j.jfa.2025.111260","DOIUrl":"10.1016/j.jfa.2025.111260","url":null,"abstract":"<div><div>We consider the <em>n</em> eigenvalues of the complex and symplectic induced spherical ensembles, which can be realised as two-dimensional determinantal and Pfaffian Coulomb gases on the Riemann sphere under the insertion of point charges. For both cases, we show that the probability that there are no eigenvalues in a spherical cap around a pole has an asymptotic behaviour as <span><math><mi>n</mi><mo>→</mo><mo>∞</mo></math></span> of the form<span><span><span><math><mi>exp</mi><mo></mo><mo>(</mo><msub><mrow><mi>c</mi></mrow><mrow><mn>1</mn></mrow></msub><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><msub><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msub><mi>n</mi><mi>log</mi><mo></mo><mi>n</mi><mo>+</mo><msub><mrow><mi>c</mi></mrow><mrow><mn>3</mn></mrow></msub><mi>n</mi><mo>+</mo><msub><mrow><mi>c</mi></mrow><mrow><mn>4</mn></mrow></msub><msqrt><mrow><mi>n</mi></mrow></msqrt><mo>+</mo><msub><mrow><mi>c</mi></mrow><mrow><mn>5</mn></mrow></msub><mi>log</mi><mo></mo><mi>n</mi><mo>+</mo><msub><mrow><mi>c</mi></mrow><mrow><mn>6</mn></mrow></msub><mo>+</mo><mi>O</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mo>−</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>12</mn></mrow></mfrac></mrow></msup><mo>)</mo><mo>)</mo><mo>,</mo></math></span></span></span> and we determine the coefficients explicitly. Our results provide the second example of precise (up to and including the constant term) large gap asymptotic behaviours for a two-dimensional point process, following a recent breakthrough by Charlier.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 4","pages":"Article 111260"},"PeriodicalIF":1.6,"publicationDate":"2026-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145464987","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 : 2026-02-15Epub Date: 2025-11-04DOI: 10.1016/j.jfa.2025.111257
Stephen Cameron , Ke Chen , Ruilin Hu , Quoc-Hung Nguyen , Yiran Xu
In this paper, we establish local well-posedness results for the Muskat equation in any dimension using modulus of continuity techniques. By introducing a novel quantity which encapsulates local monotonicity and slope, we identify a new class of initial data within . This includes scenarios where the product of the maximal and minimal slopes is large, thereby guaranteeing the local existence of a classical solution.
{"title":"The Muskat problem with a large slope","authors":"Stephen Cameron , Ke Chen , Ruilin Hu , Quoc-Hung Nguyen , Yiran Xu","doi":"10.1016/j.jfa.2025.111257","DOIUrl":"10.1016/j.jfa.2025.111257","url":null,"abstract":"<div><div>In this paper, we establish local well-posedness results for the Muskat equation in any dimension using modulus of continuity techniques. By introducing a novel quantity <span><math><msub><mrow><mi>β</mi></mrow><mrow><mi>σ</mi></mrow></msub><mo>(</mo><msubsup><mrow><mi>f</mi></mrow><mrow><mn>0</mn></mrow><mrow><mo>′</mo></mrow></msubsup><mo>)</mo></math></span> which encapsulates local monotonicity and slope, we identify a new class of initial data within <span><math><msup><mrow><mi>W</mi></mrow><mrow><mn>1</mn><mo>,</mo><mo>∞</mo></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>)</mo></math></span>. This includes scenarios where the product of the maximal and minimal slopes is large, thereby guaranteeing the local existence of a classical solution.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 4","pages":"Article 111257"},"PeriodicalIF":1.6,"publicationDate":"2026-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145518720","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 : 2026-02-15Epub Date: 2025-11-04DOI: 10.1016/j.jfa.2025.111265
Robert Fulsche , Franz Luef , Reinhard F. Werner
We investigate Wiener's Tauberian theorem from the perspective of limit functions, which results in several new versions of the Tauberian theorem. Based on this, we formulate and prove analogous Tauberian theorems for operators in the sense of quantum harmonic analysis. Using these results, we characterize the class of slowly oscillating operators and show that this class is strictly larger than the class of uniformly continuous operators. Finally, we discuss uniform versions of Wiener's Tauberian theorem and its operator analogue and provide an application of this in operator theory.
{"title":"Wiener's Tauberian theorem in classical and quantum harmonic analysis","authors":"Robert Fulsche , Franz Luef , Reinhard F. Werner","doi":"10.1016/j.jfa.2025.111265","DOIUrl":"10.1016/j.jfa.2025.111265","url":null,"abstract":"<div><div>We investigate Wiener's Tauberian theorem from the perspective of <em>limit functions</em>, which results in several new versions of the Tauberian theorem. Based on this, we formulate and prove analogous Tauberian theorems for operators in the sense of <em>quantum harmonic analysis</em>. Using these results, we characterize the class of <em>slowly oscillating operators</em> and show that this class is strictly larger than the class of uniformly continuous operators. Finally, we discuss uniform versions of Wiener's Tauberian theorem and its operator analogue and provide an application of this in operator theory.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 4","pages":"Article 111265"},"PeriodicalIF":1.6,"publicationDate":"2026-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145518714","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}
In this paper we study the dispersive properties of a two dimensional massless Dirac equation perturbed by an Aharonov–Bohm magnetic field. Our main results will be a family of pointwise decay estimates and a full range family Strichartz estimates for the flow. The proof relies on the use of a relativistic Hankel transform, which allows for an explicit representation of the propagator in terms of the generalized eigenfunctions of the operator. These results represent the natural continuation of earlier research on evolution equations associated to operators with magnetic fields with strong singularities (see [21], [36], [37] where the Schrödinger and the wave equations were studied). Indeed, we recall the fact that the Aharonov–Bohm field represents a perturbation which is critical with respect to the scaling: this fact, as it is well known, makes the analysis particularly challenging.
{"title":"Dispersive estimates for Dirac equations in Aharonov-Bohm magnetic fields: Massless case","authors":"Federico Cacciafesta , Piero D'Ancona , Zhiqing Yin , Junyong Zhang","doi":"10.1016/j.jfa.2025.111267","DOIUrl":"10.1016/j.jfa.2025.111267","url":null,"abstract":"<div><div>In this paper we study the dispersive properties of a two dimensional massless Dirac equation perturbed by an Aharonov–Bohm magnetic field. Our main results will be a family of pointwise decay estimates and a full range family Strichartz estimates for the flow. The proof relies on the use of a relativistic Hankel transform, which allows for an explicit representation of the propagator in terms of the generalized eigenfunctions of the operator. These results represent the natural continuation of earlier research on evolution equations associated to operators with magnetic fields with strong singularities (see <span><span>[21]</span></span>, <span><span>[36]</span></span>, <span><span>[37]</span></span> where the Schrödinger and the wave equations were studied). Indeed, we recall the fact that the Aharonov–Bohm field represents a perturbation which is critical with respect to the scaling: this fact, as it is well known, makes the analysis particularly challenging.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 4","pages":"Article 111267"},"PeriodicalIF":1.6,"publicationDate":"2026-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145518715","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 : 2026-02-15Epub Date: 2025-11-10DOI: 10.1016/j.jfa.2025.111271
Hui Li , Ning Liu , Weiren Zhao
In this paper, we study the stability threshold for the two-dimensional Couette flow in the whole plane. Our main result establishes that the asymptotic stability threshold is at most for Sobolev perturbations with additional control over low horizontal frequencies, aligning with the threshold results in periodic domains. As a secondary outcome of our approach, we also prove the asymptotic stability for perturbations in weak Sobolev regularity with size .
{"title":"Stability threshold of the two-dimensional Couette flow in the whole plane","authors":"Hui Li , Ning Liu , Weiren Zhao","doi":"10.1016/j.jfa.2025.111271","DOIUrl":"10.1016/j.jfa.2025.111271","url":null,"abstract":"<div><div>In this paper, we study the stability threshold for the two-dimensional Couette flow in the whole plane. Our main result establishes that the asymptotic stability threshold is at most <span><math><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac><mo>+</mo></math></span> for Sobolev perturbations with additional control over low horizontal frequencies, aligning with the threshold results in periodic domains. As a secondary outcome of our approach, we also prove the asymptotic stability for perturbations in weak Sobolev regularity with size <span><math><msup><mrow><mi>ν</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup></math></span>.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 4","pages":"Article 111271"},"PeriodicalIF":1.6,"publicationDate":"2026-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145518718","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 : 2026-02-15Epub Date: 2025-11-04DOI: 10.1016/j.jfa.2025.111256
Are Austad , David Kyed
We study the quantum metric structure arising from length functions on quantum groups and show that for coamenable quantum groups of Kac type, the quantum metric information is captured by the algebra of central functions. Using this, we provide the first examples of length functions on (genuine) quantum groups which give rise to compact quantum metric spaces.
{"title":"Quantum metrics from length functions on quantum groups","authors":"Are Austad , David Kyed","doi":"10.1016/j.jfa.2025.111256","DOIUrl":"10.1016/j.jfa.2025.111256","url":null,"abstract":"<div><div>We study the quantum metric structure arising from length functions on quantum groups and show that for coamenable quantum groups of Kac type, the quantum metric information is captured by the algebra of central functions. Using this, we provide the first examples of length functions on (genuine) quantum groups which give rise to compact quantum metric spaces.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 4","pages":"Article 111256"},"PeriodicalIF":1.6,"publicationDate":"2026-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145464985","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 : 2026-02-15Epub Date: 2025-11-04DOI: 10.1016/j.jfa.2025.111255
Paata Ivanisvili , Haonan Zhang
A recent discovery of Eldan and Gross states that there exists a universal such that for all Boolean functions , where is the sensitivity of f at x, is the variance of f, is the influence of f along the j-th variable, and μ is the uniform probability measure. In this note, we give an alternative proof that applies to biased discrete hypercube, and spaces having positive Ricci curvature lower bounds in the sense of Bakry and Émery.
{"title":"On the Eldan–Gross inequality","authors":"Paata Ivanisvili , Haonan Zhang","doi":"10.1016/j.jfa.2025.111255","DOIUrl":"10.1016/j.jfa.2025.111255","url":null,"abstract":"<div><div>A recent discovery of Eldan and Gross states that there exists a universal <span><math><mi>C</mi><mo>></mo><mn>0</mn></math></span> such that for all Boolean functions <span><math><mi>f</mi><mo>:</mo><msup><mrow><mo>{</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></mrow><mrow><mi>n</mi></mrow></msup><mo>→</mo><mo>{</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></span>,<span><span><span><math><munder><mo>∫</mo><mrow><msup><mrow><mo>{</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></mrow><mrow><mi>n</mi></mrow></msup></mrow></munder><msqrt><mrow><msub><mrow><mi>s</mi></mrow><mrow><mi>f</mi></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo></mrow></msqrt><mi>d</mi><mi>μ</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>≥</mo><mi>C</mi><mtext>Var</mtext><mo>(</mo><mi>f</mi><mo>)</mo><msqrt><mrow><mi>log</mi><mo></mo><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mfrac><mrow><mn>1</mn></mrow><mrow><msubsup><mrow><mo>∑</mo></mrow><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>n</mi></mrow></msubsup><msub><mrow><mtext>Inf</mtext></mrow><mrow><mi>j</mi></mrow></msub><msup><mrow><mo>(</mo><mi>f</mi><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac><mo>)</mo></mrow></mrow></msqrt></math></span></span></span> where <span><math><msub><mrow><mi>s</mi></mrow><mrow><mi>f</mi></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo></math></span> is the sensitivity of <em>f</em> at <em>x</em>, <span><math><mtext>Var</mtext><mo>(</mo><mi>f</mi><mo>)</mo></math></span> is the variance of <em>f</em>, <span><math><msub><mrow><mtext>Inf</mtext></mrow><mrow><mi>j</mi></mrow></msub><mo>(</mo><mi>f</mi><mo>)</mo></math></span> is the influence of <em>f</em> along the <em>j</em>-th variable, and <em>μ</em> is the uniform probability measure. In this note, we give an alternative proof that applies to biased discrete hypercube, and spaces having positive Ricci curvature lower bounds in the sense of Bakry and Émery.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 4","pages":"Article 111255"},"PeriodicalIF":1.6,"publicationDate":"2026-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145464990","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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