Journal of Functional Analysis最新文献

{"title":"Holomorphic induction beyond the norm-continuous setting, with applications to positive energy representations","authors":"Milan Niestijl","doi":"10.1016/j.jfa.2026.111382","DOIUrl":"10.1016/j.jfa.2026.111382","url":null,"abstract":"<div><div>We extend the theory of holomorphic induction of unitary representations of a possibly infinite-dimensional Lie group <em>G</em> beyond the setting where the representation being induced is required to be norm-continuous. We allow the group <em>G</em> to be a connected BCH (Baker–Campbell–Hausdorff) Fréchet–Lie group. Given a smooth <span><math><mi>R</mi></math></span>-action <em>α</em> on <em>G</em>, we proceed to show that the corresponding class of so-called positive energy representations is intimately related with holomorphic induction. Assuming that <em>G</em> is regular, we in particular show that if <em>ρ</em> is a unitary ground state representation of <span><math><mi>G</mi><msub><mrow><mo>⋊</mo></mrow><mrow><mi>α</mi></mrow></msub><mi>R</mi></math></span> for which the energy-zero subspace <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>ρ</mi></mrow></msub><mo>(</mo><mn>0</mn><mo>)</mo></math></span> admits a dense set of <em>G</em>-analytic vectors, then <span><math><msub><mrow><mi>ρ</mi><mo>|</mo></mrow><mrow><mi>G</mi></mrow></msub></math></span> is holomorphically induced from the representation of the connected subgroup <span><math><mi>H</mi><mo>:</mo><mo>=</mo><msub><mrow><mo>(</mo><msup><mrow><mi>G</mi></mrow><mrow><mi>α</mi></mrow></msup><mo>)</mo></mrow><mrow><mn>0</mn></mrow></msub></math></span> of <em>α</em>-fixed points on <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>ρ</mi></mrow></msub><mo>(</mo><mn>0</mn><mo>)</mo></math></span>. As a consequence, we obtain an isomorphism <span><math><mi>B</mi><msup><mrow><mo>(</mo><msub><mrow><mi>H</mi></mrow><mrow><mi>ρ</mi></mrow></msub><mo>)</mo></mrow><mrow><mi>G</mi></mrow></msup><mo>≅</mo><mi>B</mi><msup><mrow><mo>(</mo><msub><mrow><mi>H</mi></mrow><mrow><mi>ρ</mi></mrow></msub><mo>(</mo><mn>0</mn><mo>)</mo><mo>)</mo></mrow><mrow><mi>H</mi></mrow></msup></math></span> between the corresponding commutants. We also find that two such ground state representations are unitarily equivalent if and only if their energy-zero subspaces are unitarily equivalent as <em>H</em>-representations. These results were previously only available under the assumption of norm-continuity of the <em>H</em>-representation on <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>ρ</mi></mrow></msub><mo>(</mo><mn>0</mn><mo>)</mo></math></span>.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 9","pages":"Article 111382"},"PeriodicalIF":1.6,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146076938","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":"Degenerate or singular parabolic systems with partially DMO coefficients: the Dirichlet problem","authors":"Hongjie Dong ,&nbsp;Seongmin Jeon","doi":"10.1016/j.jfa.2026.111365","DOIUrl":"10.1016/j.jfa.2026.111365","url":null,"abstract":"<div><div>In this paper, we study solutions <em>u</em> of parabolic systems in divergence form with zero Dirichlet boundary conditions in the upper-half cylinder <span><math><msubsup><mrow><mi>Q</mi></mrow><mrow><mn>1</mn></mrow><mrow><mo>+</mo></mrow></msubsup><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup></math></span>, where the coefficients are weighted by <span><math><msubsup><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow><mrow><mi>α</mi></mrow></msubsup></math></span>, <span><math><mi>α</mi><mo>∈</mo><mo>(</mo><mo>−</mo><mo>∞</mo><mo>,</mo><mn>1</mn><mo>)</mo></math></span>. We establish higher-order boundary Schauder type estimates of <span><math><msubsup><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow><mrow><mi>α</mi></mrow></msubsup><mi>u</mi></math></span> under the assumption that the coefficients have partially Dini mean oscillation. As an application, we also achieve higher-order boundary Harnack principles for degenerate or singular equations with Hölder continuous coefficients.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 9","pages":"Article 111365"},"PeriodicalIF":1.6,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146076934","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":"Half-space Liouville-type theorems for minimal graphs with capillary boundary","authors":"Guofang Wang ,&nbsp;Wei Wei ,&nbsp;Xuwen Zhang","doi":"10.1016/j.jfa.2026.111366","DOIUrl":"10.1016/j.jfa.2026.111366","url":null,"abstract":"<div><div>In this paper, we prove two Liouville-type theorems for capillary minimal graph over <span><math><msubsup><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow><mrow><mi>n</mi></mrow></msubsup></math></span>. First, if <em>u</em> has linear growth, then for <span><math><mi>n</mi><mo>=</mo><mn>2</mn><mo>,</mo><mn>3</mn></math></span> and for any <span><math><mi>θ</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mi>π</mi><mo>)</mo></math></span>, or <span><math><mi>n</mi><mo>≥</mo><mn>4</mn></math></span> and <span><math><mi>θ</mi><mo>∈</mo><mo>(</mo><mfrac><mrow><mi>π</mi></mrow><mrow><mn>6</mn></mrow></mfrac><mo>,</mo><mfrac><mrow><mn>5</mn><mi>π</mi></mrow><mrow><mn>6</mn></mrow></mfrac><mo>)</mo></math></span>, <em>u</em> must be flat. Second, if <em>u</em> is one-sided bounded on <span><math><msubsup><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow><mrow><mi>n</mi></mrow></msubsup></math></span>, then for any <em>n</em> and <span><math><mi>θ</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mi>π</mi><mo>)</mo></math></span>, <em>u</em> must be flat. The proofs build upon gradient estimates for the mean curvature equation over <span><math><msubsup><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow><mrow><mi>n</mi></mrow></msubsup></math></span> with capillary boundary condition, which are based on carefully adapting the maximum principle to the capillary setting.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 9","pages":"Article 111366"},"PeriodicalIF":1.6,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146190805","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 the log-Sobolev constant of log-concave vectors","authors":"Pierre Bizeul","doi":"10.1016/j.jfa.2026.111368","DOIUrl":"10.1016/j.jfa.2026.111368","url":null,"abstract":"<div><div>It is well known that if a random vector satisfies a log-Sobolev inequality, all of its marginals have subgaussian tails. In the spirit of the KLS conjecture, we investigate whether this implication can be reversed under a log-concavity assumption. In the general setting, we improve on a result of Bobkov, establishing the best dimension dependent bound on the log-Sobolev constant of subgaussian log-concave measures, and we investigate some special cases.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 9","pages":"Article 111368"},"PeriodicalIF":1.6,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146190806","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 character correspondence in the stable range over a p-adic field","authors":"Hung Yean Loke ,&nbsp;Tomasz Przebinda","doi":"10.1016/j.jfa.2026.111392","DOIUrl":"10.1016/j.jfa.2026.111392","url":null,"abstract":"<div><div>Given a real irreducible dual pair there is an integral kernel operator which maps the distribution character of an irreducible admissible representation of the group with the smaller or equal rank to an invariant eigendistribution on the group with the larger or equal rank. If the pair is in the stable range and if the representation is unitary, then the resulting distribution is the character of the representation obtained via Howe's correspondence. This construction was transferred to the p-adic case and a conjecture was formulated.</div><div>In this note we verify a weaker version of this conjecture for dual pairs in the stable range over a p-adic field.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 9","pages":"Article 111392"},"PeriodicalIF":1.6,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146190807","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 characterization of generalized functions of bounded deformation","authors":"Antonin Chambolle ,&nbsp;Vito Crismale","doi":"10.1016/j.jfa.2026.111391","DOIUrl":"10.1016/j.jfa.2026.111391","url":null,"abstract":"<div><div>We show that Dal Maso's <em>GBD</em> space, introduced for tackling crack growth in linearized elasticity, can be defined by simple conditions in a finite number of directions of slicing.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 9","pages":"Article 111391"},"PeriodicalIF":1.6,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146190810","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":"Global well-posedness and density patches for liquid crystal system","authors":"Qionglei Chen ,&nbsp;Xiaonan Hao ,&nbsp;Omar Lazar","doi":"10.1016/j.jfa.2026.111356","DOIUrl":"10.1016/j.jfa.2026.111356","url":null,"abstract":"<div><div>We prove a global well-posedness result for a liquid crystal system with bounded but arbitrarily large density and velocity. Applying the Lagrangian approach with more refined estimates we are able to not only work in the critical regularity space but also to overcome the difficulty arising from the fact that we are dealing with a coupled hyperbolic system. Taking advantage of our uniqueness result, we study the density patches problem by using classical techniques, namely, Littlewood-Paley multipliers together with the smoothing effect of the Newtonian potential and on certain symmetry property motivated by <span><span>[13]</span></span>. One of the key point of the proof is to introduce the material derivative and perform more refined estimates for the direction field.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 8","pages":"Article 111356"},"PeriodicalIF":1.6,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146036486","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 note on the stability of self-similar blow-up solutions for superconformal semilinear wave equations","authors":"Jie Liu","doi":"10.1016/j.jfa.2026.111364","DOIUrl":"10.1016/j.jfa.2026.111364","url":null,"abstract":"<div><div>In this note, we investigate the stability of self-similar blow-up solutions for superconformal semilinear wave equations in all dimensions. A central aspect of our analysis is the spectral equivalence of the linearized operators under Lorentz transformations in self-similar variables. This observation serves as a useful tool in proving mode stability and provides insights that may aid the study of self-similar solutions in related problems. As a direct consequence, we establish the asymptotic stability of the ODE blow-up family, extending the classical results of Merle and Zaag <span><span>[45]</span></span>, <span><span>[51]</span></span> to the conformal and superconformal regimes and generalizing the recent work of Ostermann <span><span>[52]</span></span> to include the entire ODE blow-up family.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 8","pages":"Article 111364"},"PeriodicalIF":1.6,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146036487","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":"Conformal and extrinsic upper bounds for the harmonic mean of Neumann and Steklov eigenvalues","authors":"Hang Chen","doi":"10.1016/j.jfa.2026.111361","DOIUrl":"10.1016/j.jfa.2026.111361","url":null,"abstract":"<div><div>Let <em>M</em> be an <em>m</em>-dimensional compact Riemannian manifold with boundary. We obtain the upper bounds of the harmonic mean of the first <em>m</em> nonzero Neumann eigenvalues and Steklov eigenvalues involving the conformal volume and relative conformal volume, respectively. We also give an optimal sharp extrinsic upper bound for closed submanifolds in space forms. These extend the previous related results for the first nonzero eigenvalues.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 8","pages":"Article 111361"},"PeriodicalIF":1.6,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146036488","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":"Existence of solutions to the fractional semilinear heat equation with a singular inhomogeneous term","authors":"Kazuhiro Ishige ,&nbsp;Tatsuki Kawakami ,&nbsp;Ryo Takada","doi":"10.1016/j.jfa.2026.111352","DOIUrl":"10.1016/j.jfa.2026.111352","url":null,"abstract":"<div><div>We study the existence of solutions to the fractional semilinear heat equation with a singular inhomogeneous term. For this aim, we establish decay estimates of the fractional heat semigroup in several uniformly local Zygumnd spaces. Furthermore, we apply the real interpolation method in uniformly local Zygmund spaces to obtain sharp integral estimates on the inhomogeneous term and the nonlinear term. This enables us to find sharp sufficient conditions for the existence of solutions to the fractional semilinear heat equation with a singular inhomogeneous term.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 8","pages":"Article 111352"},"PeriodicalIF":1.6,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146036480","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}