Journal of Functional Analysis最新文献

{"title":"On C1 Whitney extension theorem in Banach spaces","authors":"Michal Johanis,&nbsp;Luděk Zajíček","doi":"10.1016/j.jfa.2025.111061","DOIUrl":"10.1016/j.jfa.2025.111061","url":null,"abstract":"<div><div>Our note is a complement to recent articles <span><span>[17]</span></span> (2011) and <span><span>[18]</span></span> (2013) by M. Jiménez-Sevilla and L. Sánchez-González which generalise (the basic statement of) the classical Whitney extension theorem for <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-smooth real functions on <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> to the case of real functions on <em>X</em> (<span><span>[17]</span></span>) and to the case of mappings from <em>X</em> to <em>Y</em> (<span><span>[18]</span></span>) for some Banach spaces <em>X</em> and <em>Y</em>. Since the proof from <span><span>[18]</span></span> contains a serious flaw, we supply a different more transparent detailed proof under (probably) slightly stronger assumptions on <em>X</em> and <em>Y</em>. Our proof gives also extensions results from special sets (e.g. Lipschitz submanifolds or closed convex bodies) under substantially weaker assumptions on <em>X</em> and <em>Y</em>. Further, we observe that the mapping <span><math><mi>F</mi><mo>∈</mo><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>(</mo><mi>X</mi><mo>;</mo><mi>Y</mi><mo>)</mo></math></span> which extends <em>f</em> given on a closed set <span><math><mi>A</mi><mo>⊂</mo><mi>X</mi></math></span> can be, in some cases, <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span>-smooth (or <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>k</mi></mrow></msup></math></span>-smooth with <span><math><mi>k</mi><mo>&gt;</mo><mn>1</mn></math></span>) on <span><math><mi>X</mi><mo>∖</mo><mi>A</mi></math></span>. Of course, also this improved result is weaker than Whitney's result (for <span><math><mi>X</mi><mo>=</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>, <span><math><mi>Y</mi><mo>=</mo><mi>R</mi></math></span>) which asserts that <em>F</em> is even analytic on <span><math><mi>X</mi><mo>∖</mo><mi>A</mi></math></span>. Further, following another Whitney's article and using the above results, we prove results on extensions of <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-smooth mappings from open (“weakly”) quasiconvex subsets of <em>X</em>. Following the above mentioned articles <span><span>[17]</span></span>, <span><span>[18]</span></span> we also consider the question concerning the Lipschitz constant of <em>F</em> if <em>f</em> is a Lipschitz mapping.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 9","pages":"Article 111061"},"PeriodicalIF":1.7,"publicationDate":"2025-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144203144","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":"New pointwise bounds by Riesz potential type operators","authors":"Cong Hoang ,&nbsp;Kabe Moen ,&nbsp;Carlos Pérez Moreno","doi":"10.1016/j.jfa.2025.111060","DOIUrl":"10.1016/j.jfa.2025.111060","url":null,"abstract":"<div><div>We investigate new pointwise bounds for a class of rough integral operators, <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>Ω</mi><mo>,</mo><mi>α</mi></mrow></msub></math></span>, for a parameter <span><math><mn>0</mn><mo>&lt;</mo><mi>α</mi><mo>&lt;</mo><mi>n</mi></math></span> that includes classical rough singular integrals of Calderón and Zygmund, rough hypersingular integrals, and rough fractional integral operators. We prove that the rough integral operators are bounded by a sparse potential operator that depends on the size of the symbol Ω. As a result of our pointwise inequalities, we obtain several new Sobolev mappings of the form <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>Ω</mi><mo>,</mo><mi>α</mi></mrow></msub><mo>:</mo><msup><mrow><mover><mrow><mi>W</mi></mrow><mrow><mo>˙</mo></mrow></mover></mrow><mrow><mn>1</mn><mo>,</mo><mi>p</mi></mrow></msup><mo>→</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>q</mi></mrow></msup></math></span>.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 9","pages":"Article 111060"},"PeriodicalIF":1.7,"publicationDate":"2025-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144203145","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":"Spectral estimate for the Laplace–Beltrami operator on the hyperbolic half-plane","authors":"Marc Rouveyrol","doi":"10.1016/j.jfa.2025.111059","DOIUrl":"10.1016/j.jfa.2025.111059","url":null,"abstract":"<div><div>The purpose of this note is to investigate the concentration properties of spectral projectors on manifolds. This question has been intensively studied (by Logvinenko–Sereda, Nazarov, Jerison–Lebeau, Kovrizhkin, Egidi–Seelmann–Veselić, Burq–Moyano, among others) in connection with the uncertainty principle. We provide the first high-frequency results in a geometric setting which is neither Euclidean nor a perturbation of Euclidean. Namely, we prove the natural (and optimal) uncertainty principle for the spectral projector on the hyperbolic half-plane.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 8","pages":"Article 111059"},"PeriodicalIF":1.7,"publicationDate":"2025-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144138044","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 loss and propagation of modulus of continuity for the two-dimensional incompressible Euler equations","authors":"Karim R. Shikh Khalil","doi":"10.1016/j.jfa.2025.111066","DOIUrl":"10.1016/j.jfa.2025.111066","url":null,"abstract":"<div><div>It is known from the work of Koch that the two-dimensional incompressible Euler equations propagate Dini modulus of continuity for the vorticity. In this work, we consider the two-dimensional Euler equations with a modulus of continuity for vorticity rougher than Dini continuous. We first show that the two-dimensional Euler equations propagate an explicit family of moduli of continuity for the vorticity that are rougher than Dini continuity. The main goal of this work is to address the following question: Given a modulus of continuity for the 2D Euler equations, can we always propagate it? The answer to this question is No. We construct a family of moduli of continuity for the 2D Euler equations that are not propagated.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 8","pages":"Article 111066"},"PeriodicalIF":1.7,"publicationDate":"2025-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144138045","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":"Local Blaschke–Kakutani ellipsoid characterization and Banach's isometric subspaces problem","authors":"Sergei Ivanov ,&nbsp;Daniil Mamaev ,&nbsp;Anya Nordskova","doi":"10.1016/j.jfa.2025.111063","DOIUrl":"10.1016/j.jfa.2025.111063","url":null,"abstract":"<div><div>We prove the following local version of Blaschke–Kakutani's characterization of ellipsoids: Let <em>V</em> be a finite-dimensional real vector space, <span><math><mi>B</mi><mo>⊂</mo><mi>V</mi></math></span> a convex body with 0 in its interior, and <span><math><mn>2</mn><mo>≤</mo><mi>k</mi><mo>&lt;</mo><mi>dim</mi><mo>⁡</mo><mi>V</mi></math></span> an integer. Suppose that the body <em>B</em> is contained in a cylinder based on the cross-section <span><math><mi>B</mi><mo>∩</mo><mi>X</mi></math></span> for every <em>k</em>-plane <em>X</em> from a connected open set of linear <em>k</em>-planes in <em>V</em>. Then in the region of <em>V</em> swept by these <em>k</em>-planes <em>B</em> coincides with either an ellipsoid, or a cylinder over an ellipsoid, or a cylinder over a <em>k</em>-dimensional base.</div><div>For <span><math><mi>k</mi><mo>=</mo><mn>2</mn></math></span> and <span><math><mi>k</mi><mo>=</mo><mn>3</mn></math></span> we obtain as a corollary a local solution to Banach's isometric subspaces problem: If all cross-sections of <em>B</em> by <em>k</em>-planes from a connected open set are linearly equivalent, then the same conclusion as above holds.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 8","pages":"Article 111063"},"PeriodicalIF":1.7,"publicationDate":"2025-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144169796","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":"Compact T(1) theorem à la Stein","authors":"Árpád Bényi ,&nbsp;Guopeng Li ,&nbsp;Tadahiro Oh ,&nbsp;Rodolfo H. Torres","doi":"10.1016/j.jfa.2025.111052","DOIUrl":"10.1016/j.jfa.2025.111052","url":null,"abstract":"<div><div>We prove a compact <span><math><mi>T</mi><mo>(</mo><mn>1</mn><mo>)</mo></math></span> theorem, involving quantitative estimates, analogous to the quantitative classical <span><math><mi>T</mi><mo>(</mo><mn>1</mn><mo>)</mo></math></span> theorem due to Stein. We also discuss the <span><math><msubsup><mrow><mi>C</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>∞</mo></mrow></msubsup></math></span>-to-<em>CMO</em> mapping properties of non-compact Calderón-Zygmund operators as well as the sequential completeness properties of some subspaces of <em>BMO</em> under different topologies.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 7","pages":"Article 111052"},"PeriodicalIF":1.7,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144106611","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":"Shift invariant subspaces of large index in the Bloch space","authors":"Nikiforos Biehler","doi":"10.1016/j.jfa.2025.111034","DOIUrl":"10.1016/j.jfa.2025.111034","url":null,"abstract":"<div><div>We consider the shift operator <span><math><msub><mrow><mi>M</mi></mrow><mrow><mi>z</mi></mrow></msub></math></span>, defined on the Bloch space and the little Bloch space and we study the corresponding lattice of invariant subspaces. We construct closed, shift invariant subspaces in the Bloch space and the little Bloch space that can have arbitrarily large, but countable, index. On the non-separable Bloch space we construct a closed shift invariant subspace with cardinality equal to the unit interval. Finally we establish several results on the index for the weak-star topology of a Banach space and prove a stability theorem for the index when passing from (norm closed) invariant subspaces of a Banach space to their weak-star closure in its second dual. This is then applied to prove the existence of weak-star closed invariant subspaces of arbitrary index in the Bloch space.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 7","pages":"Article 111034"},"PeriodicalIF":1.7,"publicationDate":"2025-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143923574","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":"Prescribing positive curvature with conical singularities on S2","authors":"Jingyi Chen ,&nbsp;Yuxiang Li ,&nbsp;Yunqing Wu","doi":"10.1016/j.jfa.2025.111031","DOIUrl":"10.1016/j.jfa.2025.111031","url":null,"abstract":"<div><div>For conformal metrics with conical singularities and positive curvature on <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>, we prove a convergence theorem and apply it to obtain a criterion for nonexistence in an open region of the prescribing data. The core of our study is a fine analysis of the bubble trees and an area identity in the convergence process.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 6","pages":"Article 111031"},"PeriodicalIF":1.7,"publicationDate":"2025-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143895124","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 closability of differential operators","authors":"Giovanni Alberti ,&nbsp;David Bate ,&nbsp;Andrea Marchese","doi":"10.1016/j.jfa.2025.111029","DOIUrl":"10.1016/j.jfa.2025.111029","url":null,"abstract":"<div><div>We discuss the closability of directional derivative operators with respect to a general Radon measure <em>μ</em> on <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>; our main theorem completely characterizes the vectorfields for which the corresponding operator is closable from the space of Lipschitz functions <span><math><mrow><mi>Lip</mi></mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>)</mo></math></span> to <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><mi>μ</mi><mo>)</mo></math></span>, for <span><math><mn>1</mn><mo>≤</mo><mi>p</mi><mo>≤</mo><mo>∞</mo></math></span>. We also discuss the closability of the same operators from <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>q</mi></mrow></msup><mo>(</mo><mi>μ</mi><mo>)</mo></math></span> to <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><mi>μ</mi><mo>)</mo></math></span>, and give necessary and sufficient conditions for closability, but we do not have an exact characterization.</div><div>As a corollary we obtain that classical differential operators such as gradient, divergence and Jacobian determinant are closable from <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>q</mi></mrow></msup><mo>(</mo><mi>μ</mi><mo>)</mo></math></span> to <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><mi>μ</mi><mo>)</mo></math></span> only if <em>μ</em> is absolutely continuous with respect to the Lebesgue measure.</div><div>We finally consider the closability of a certain class of multilinear differential operators; these results are then rephrased in terms of metric currents.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 7","pages":"Article 111029"},"PeriodicalIF":1.7,"publicationDate":"2025-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143923573","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 continuity of Følner averages","authors":"Gabriel Fuhrmann ,&nbsp;Maik Gröger ,&nbsp;Till Hauser","doi":"10.1016/j.jfa.2025.111039","DOIUrl":"10.1016/j.jfa.2025.111039","url":null,"abstract":"<div><div>It is known that if each point <em>x</em> of a dynamical system is generic for some invariant measure <span><math><msub><mrow><mi>μ</mi></mrow><mrow><mi>x</mi></mrow></msub></math></span>, then there is a strong connection between certain ergodic and topological properties of that system. In particular, if the acting group is abelian and the map <span><math><mi>x</mi><mo>↦</mo><msub><mrow><mi>μ</mi></mrow><mrow><mi>x</mi></mrow></msub></math></span> is continuous, then every orbit closure is uniquely ergodic.</div><div>In this note, we show that if the acting group is not abelian, orbit closures may well support more than one ergodic measure even if <span><math><mi>x</mi><mo>↦</mo><msub><mrow><mi>μ</mi></mrow><mrow><mi>x</mi></mrow></msub></math></span> is continuous. We provide examples of such a situation via actions of the group of all orientation-preserving homeomorphisms on the unit interval as well as the Lamplighter group. To discuss these examples, we need to extend the existing theory of weakly mean equicontinuous group actions to allow for multiple ergodic measures on orbit closures and to allow for actions of general amenable groups. These extensions are achieved by adopting an operator-theoretic approach.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 7","pages":"Article 111039"},"PeriodicalIF":1.7,"publicationDate":"2025-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143942789","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}