Journal of Functional Analysis最新文献

{"title":"Nonlocal H-convergence for topologically nontrivial domains","authors":"Marcus Waurick","doi":"10.1016/j.jfa.2024.110710","DOIUrl":"10.1016/j.jfa.2024.110710","url":null,"abstract":"<div><div>The notion of nonlocal <em>H</em>-convergence is extended to domains with nontrivial topology, that is, domains with non-vanishing harmonic Dirichlet and/or Neumann fields. If the space of harmonic Dirichlet (or Neumann) fields is infinite-dimensional, there is an abundance of choice of pairwise incomparable topologies generalising the one for topologically trivial Ω. It will be demonstrated that if the domain satisfies the Maxwell compactness property the corresponding natural version of the corresponding (generalised) nonlocal <em>H</em>-convergence topology has no such ambiguity. Moreover, on multiplication operators the nonlocal <em>H</em>-topology coincides with the one induced by (local) <em>H</em>-convergence introduced by Murat and Tartar. The topology is used to obtain nonlocal homogenisation results including convergence of the associated energy for electrostatics. The derived techniques prove useful to deduce a new compactness criterion relevant for nonlinear static Maxwell problems.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142551912","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":"On the amenable subalgebras of group von Neumann algebras","authors":"Tattwamasi Amrutam ,&nbsp;Yair Hartman ,&nbsp;Hanna Oppelmayer","doi":"10.1016/j.jfa.2024.110718","DOIUrl":"10.1016/j.jfa.2024.110718","url":null,"abstract":"<div><div>We approach the study of sub-von Neumann algebras of the group von Neumann algebra <span><math><mi>L</mi><mo>(</mo><mi>Γ</mi><mo>)</mo></math></span> for countable groups Γ from a dynamical perspective. It is shown that <span><math><mi>L</mi><mo>(</mo><mi>Γ</mi><mo>)</mo></math></span> admits a maximal invariant amenable subalgebra. The notion of invariant probability measures (IRAs) on the space of subalgebras is introduced, analogous to the concept of Invariant Random Subgroups. And it is shown that amenable IRAs are supported on the maximal amenable invariant subalgebra.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142554255","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 expansiveness of coarse maps between Banach spaces and geometry preservation","authors":"Bruno M. Braga ,&nbsp;Gilles Lancien","doi":"10.1016/j.jfa.2024.110724","DOIUrl":"10.1016/j.jfa.2024.110724","url":null,"abstract":"<div><div>We introduce a new notion of embeddability between Banach spaces. By studying the classical Mazur map, we show that it is strictly weaker than the notion of coarse embeddability. We use the techniques from metric cotype introduced by M. Mendel and A. Naor to prove results about cotype preservation and complete our study of embeddability between <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> spaces. We confront our notion with nonlinear invariants introduced by N. Kalton, which are defined in terms of concentration properties for Lipschitz maps defined on countably branching Hamming or interlaced graphs. Finally, we address the problem of the embeddability into <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span>.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142578183","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":"Stability of the Wulff shape with respect to anisotropic curvature functionals","authors":"Julian Scheuer ,&nbsp;Xuwen Zhang","doi":"10.1016/j.jfa.2024.110715","DOIUrl":"10.1016/j.jfa.2024.110715","url":null,"abstract":"<div><div>For a function <em>f</em> which foliates a one-sided neighborhood of a closed hypersurface <em>M</em>, we give an estimate of the distance of <em>M</em> to a Wulff shape in terms of the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>-norm of the traceless <em>F</em>-Hessian of <em>f</em>, where <em>F</em> is the support function of the Wulff shape. This theorem is applied to prove quantitative stability results for the anisotropic Heintze-Karcher inequality, the anisotropic Alexandrov problem, as well as for the anisotropic overdetermined boundary value problem of Serrin-type.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142551910","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 frequency-independent bound on trigonometric polynomials of Gaussians and applications","authors":"Fanhao Kong ,&nbsp;Wenhao Zhao","doi":"10.1016/j.jfa.2024.110705","DOIUrl":"10.1016/j.jfa.2024.110705","url":null,"abstract":"<div><div>We prove a frequency-independent bound on trigonometric functions of a class of singular Gaussian random fields, which arise naturally from weak universality problems for singular stochastic PDEs. This enables us to reduce the regularity assumption on the nonlinearity of the microscopic models (for pathwise convergence) in KPZ and dynamical <span><math><msubsup><mrow><mi>Φ</mi></mrow><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></msubsup></math></span> in the previous works of Hairer-Xu and Furlan-Gubinelli to heuristically optimal thresholds required by PDE structures.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142551913","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":"Logarithmic Sobolev inequalities for bounded domains and applications to drift-diffusion equations","authors":"Elie Abdo ,&nbsp;Fizay-Noah Lee","doi":"10.1016/j.jfa.2024.110716","DOIUrl":"10.1016/j.jfa.2024.110716","url":null,"abstract":"<div><div>We prove logarithmic Sobolev inequalities on higher-dimensional bounded smooth domains based on novel Gagliardo-Nirenberg type interpolation inequalities. Moreover, we use them to address the long-time dynamics of some nonlinear nonlocal drift-diffusion models and prove the exponential decay of their solutions to constant steady states.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142553560","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":"Duality, BMO and Hankel operators on Bernstein spaces","authors":"Carlo Bellavita ,&nbsp;Marco M. Peloso","doi":"10.1016/j.jfa.2024.110708","DOIUrl":"10.1016/j.jfa.2024.110708","url":null,"abstract":"<div><div>In this paper we deal with the problem of describing the dual space <span><math><msup><mrow><mo>(</mo><msubsup><mrow><mi>B</mi></mrow><mrow><mi>κ</mi></mrow><mrow><mn>1</mn></mrow></msubsup><mo>)</mo></mrow><mrow><mo>⁎</mo></mrow></msup></math></span> of the Bernstein space <span><math><msubsup><mrow><mi>B</mi></mrow><mrow><mi>κ</mi></mrow><mrow><mn>1</mn></mrow></msubsup></math></span>, that is the space of entire functions of exponential type (at most) <span><math><mi>κ</mi><mo>&gt;</mo><mn>0</mn></math></span> whose restriction to the real line is Lebesgue integrable. We provide several characterizations, showing that such dual space can be described as a quotient of the space of entire functions of exponential type <em>κ</em> whose restriction to the real line are in a suitable BMO-type space, or as the space of symbols <em>b</em> for which the Hankel operator <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>b</mi></mrow></msub></math></span> is bounded on the Paley–Wiener space <span><math><msubsup><mrow><mi>B</mi></mrow><mrow><mi>κ</mi><mo>/</mo><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msubsup></math></span>. We also provide a characterization of <span><math><msup><mrow><mo>(</mo><msubsup><mrow><mi>B</mi></mrow><mrow><mi>κ</mi></mrow><mrow><mn>1</mn></mrow></msubsup><mo>)</mo></mrow><mrow><mo>⁎</mo></mrow></msup></math></span> as the BMO space w.r.t. the Clark measures of the inner function <span><math><msup><mrow><mi>e</mi></mrow><mrow><mi>i</mi><mn>2</mn><mi>κ</mi><mi>z</mi></mrow></msup></math></span> on the upper half-plane, in analogy with the known description of the dual of backward-shift invariant 1-spaces on the torus. Furthermore, we show that the orthogonal projection <span><math><msub><mrow><mi>P</mi></mrow><mrow><mi>κ</mi></mrow></msub><mo>:</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mi>R</mi><mo>)</mo><mo>→</mo><msubsup><mrow><mi>B</mi></mrow><mrow><mi>κ</mi></mrow><mrow><mn>2</mn></mrow></msubsup></math></span> induces a bounded operator from <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>(</mo><mi>R</mi><mo>)</mo></math></span> onto <span><math><msup><mrow><mo>(</mo><msubsup><mrow><mi>B</mi></mrow><mrow><mi>κ</mi></mrow><mrow><mn>1</mn></mrow></msubsup><mo>)</mo></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>.</div><div>Finally, we show that <span><math><msubsup><mrow><mi>B</mi></mrow><mrow><mi>κ</mi></mrow><mrow><mn>1</mn></mrow></msubsup></math></span> is the dual space of a suitable VMO-type space or as the space of symbols <em>b</em> for which the Hankel operator <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>b</mi></mrow></msub></math></span> on the Paley–Wiener space <span><math><msubsup><mrow><mi>B</mi></mrow><mrow><mi>κ</mi><mo>/</mo><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msubsup></math></span> is compact.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142554254","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":"Sharp analytic version of Fefferman's inequality","authors":"Tomasz Gałązka,&nbsp;Adam Osękowski","doi":"10.1016/j.jfa.2024.110707","DOIUrl":"10.1016/j.jfa.2024.110707","url":null,"abstract":"<div><div>Let <span><math><mi>T</mi></math></span> be a unit circle. Assume further that <em>f</em> is an element of the Hardy space <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>(</mo><mi>T</mi><mo>)</mo></math></span> and <em>g</em> belongs to the analytic <em>BMO</em> space on <span><math><mi>T</mi></math></span>. The paper contains the identification of the optimal universal constant <em>C</em> in the estimate<span><span><span><math><mrow><mo>|</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn><mi>π</mi></mrow></mfrac><munder><mo>∫</mo><mrow><mi>T</mi></mrow></munder><mover><mrow><mi>f</mi><mo>(</mo><mi>ζ</mi><mo>)</mo></mrow><mo>‾</mo></mover><mi>g</mi><mo>(</mo><mi>ζ</mi><mo>)</mo><mtext>d</mtext><mi>ζ</mi><mo>|</mo></mrow><mo>≤</mo><mi>C</mi><mspace></mspace><msub><mrow><mo>‖</mo><mi>f</mi><mo>‖</mo></mrow><mrow><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>(</mo><mi>T</mi><mo>)</mo></mrow></msub><msub><mrow><mo>‖</mo><mi>g</mi><mo>‖</mo></mrow><mrow><mi>B</mi><mi>M</mi><mi>O</mi><mo>(</mo><mi>T</mi><mo>)</mo></mrow></msub><mo>.</mo></math></span></span></span> Actually, the inequality is studied in the stronger form, involving the Littlewood-Paley function on the left and the sharp maximal function of <em>g</em> on the right. The proof rests on the construction of an appropriate plurisuperharmonic function on a parabolic domain and the application of probabilistic techniques.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142586383","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":"Hermite expansions for spaces of functions with nearly optimal time-frequency decay","authors":"Lenny Neyt ,&nbsp;Joachim Toft ,&nbsp;Jasson Vindas","doi":"10.1016/j.jfa.2024.110706","DOIUrl":"10.1016/j.jfa.2024.110706","url":null,"abstract":"<div><div>We establish Hermite expansion characterizations for several subspaces of the Fréchet space of functions on the real line satisfying<span><span><span><math><mo>|</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>|</mo><mo>≲</mo><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo><mo>(</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>−</mo><mi>λ</mi><mo>)</mo><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></msup><mo>,</mo><mspace></mspace><mo>|</mo><mover><mrow><mi>f</mi></mrow><mrow><mo>ˆ</mo></mrow></mover><mo>(</mo><mi>ξ</mi><mo>)</mo><mo>|</mo><mo>≲</mo><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo><mo>(</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>−</mo><mi>λ</mi><mo>)</mo><msup><mrow><mi>ξ</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></msup><mo>,</mo><mspace></mspace><mo>∀</mo><mi>λ</mi><mo>&gt;</mo><mn>0</mn><mo>.</mo></math></span></span></span> In particular, we extend and improve Fourier characterizations of the so-called proper Pilipović spaces obtained in <span><span>[21]</span></span>. The main ingredients in our proofs are the Bargmann transform and some achieved optimal forms of the Phragmén-Lindelöf principle.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142560550","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":"Blowup dynamics for smooth equivariant solutions to energy critical Landau-Lifschitz flow","authors":"Jitao Xu,&nbsp;Lifeng Zhao","doi":"10.1016/j.jfa.2024.110704","DOIUrl":"10.1016/j.jfa.2024.110704","url":null,"abstract":"<div><div>In this paper, we study the energy critical 1-equivariant Landau-Lifschitz flow mapping <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> to <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> with arbitrary given coefficients <span><math><msub><mrow><mi>ρ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>∈</mo><mi>R</mi><mo>,</mo><mspace></mspace><msub><mrow><mi>ρ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>&gt;</mo><mn>0</mn></math></span>. We prove that there exists a codimension one smooth well-localized set of initial data arbitrarily close to the ground state which generates type-II finite-time blowup solutions, and give a precise description of the corresponding singularity formation. In our proof, both the Schrödinger part and the heat part play important roles in the construction of approximate solutions and the mixed energy/Morawetz functional. However, the blowup rate is independent of the coefficients.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142528660","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}