Journal of Functional Analysis最新文献

{"title":"On the uncertainty principle for metaplectic transformations","authors":"Nicolas Lerner","doi":"10.1016/j.jfa.2025.110997","DOIUrl":"10.1016/j.jfa.2025.110997","url":null,"abstract":"<div><div>This paper deals with a version of the Uncertainty Principle applied to operators in the Metaplectic group, the two-fold cover of the symplectic group. We calculate explicitly the sharp lowerbound occurring in our formulation: we provide a sharp lowerbound for the product of variances of <em>Mu</em> and of <em>u</em> for a function <em>u</em> normalized in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></math></span> and <em>M</em> a metaplectic transformation. The proofs are based upon the symplectic covariance of the Weyl calculus as well as upon some structural facts about the generators of the metaplectic group. We found some motivations in the new proofs and extensions of the Heisenberg Uncertainty Principle introduced by A. Widgerson &amp; Y. Widgerson in <span><span>[28]</span></span>, developed in <span><span>[7]</span></span> by N.C. Dias, F. Luef and J.N. Prata and also in <span><span>[24]</span></span>, <span><span>[25]</span></span> by Y. Tang.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 5","pages":"Article 110997"},"PeriodicalIF":1.7,"publicationDate":"2025-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143860171","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 Harnack type inequality for singular Liouville type equations","authors":"Paolo Cosentino","doi":"10.1016/j.jfa.2025.111003","DOIUrl":"10.1016/j.jfa.2025.111003","url":null,"abstract":"<div><div>We obtain a Harnack type inequality for solutions of the Liouville type equation,<span><span><span><math><mo>−</mo><mi>Δ</mi><mi>u</mi><mo>=</mo><mo>|</mo><mi>x</mi><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn><mi>α</mi></mrow></msup><mi>K</mi><mo>(</mo><mi>x</mi><mo>)</mo><msup><mrow><mi>e</mi></mrow><mrow><mi>u</mi></mrow></msup><mspace></mspace><mtext>in</mtext><mspace></mspace><mspace></mspace><mspace></mspace><mi>Ω</mi><mo>,</mo></math></span></span></span> where <span><math><mi>α</mi><mo>∈</mo><mo>(</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></span>, Ω is a bounded domain in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> and <em>K</em> satisfies,<span><span><span><math><mn>0</mn><mo>&lt;</mo><mi>a</mi><mo>≤</mo><mi>K</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>≤</mo><mi>b</mi><mo>&lt;</mo><mo>+</mo><mo>∞</mo><mo>.</mo></math></span></span></span> This is a generalization to the singular case of a result by Chen and Lin (1998) <span><span>[12]</span></span>, which considered the regular case <span><math><mi>α</mi><mo>=</mo><mn>0</mn></math></span>.</div><div>Part of the argument of Chen-Lin can be adapted to the singular case by means of an isoperimetric inequality for surfaces with conical singularities. However, the case <span><math><mi>α</mi><mo>∈</mo><mo>(</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></span> turns out to be more delicate, due to the lack of translation invariance of the singular problem, which requires a different approach.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 8","pages":"Article 111003"},"PeriodicalIF":1.7,"publicationDate":"2025-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143859744","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":"Low energy levels of harmonic spheres in analytic manifolds","authors":"Melanie Rupflin","doi":"10.1016/j.jfa.2025.111006","DOIUrl":"10.1016/j.jfa.2025.111006","url":null,"abstract":"<div><div>We consider the energy spectrum <span><math><msub><mrow><mi>Ξ</mi></mrow><mrow><mi>E</mi></mrow></msub><mo>(</mo><mi>N</mi><mo>)</mo></math></span> of harmonic maps from the sphere into a closed Riemannian manifold <em>N</em>. While a well known conjecture asserts that <span><math><msub><mrow><mi>Ξ</mi></mrow><mrow><mi>E</mi></mrow></msub><mo>(</mo><mi>N</mi><mo>)</mo></math></span> is discrete whenever <em>N</em> is analytic, for most analytic targets it is only known that any potential accumulation point of the energy spectrum must be given by the sum of the energies of at least two harmonic spheres. The lowest energy level that could hence potentially be an accumulation point of <span><math><msub><mrow><mi>Ξ</mi></mrow><mrow><mi>E</mi></mrow></msub></math></span> is thus <span><math><mn>2</mn><msub><mrow><mi>E</mi></mrow><mrow><mtext>min</mtext></mrow></msub></math></span>. In the present paper we exclude this possibility for generic 3 manifolds and prove additional results that establish obstructions to the gluing of harmonic spheres and provide Łojasiewicz-estimates for almost harmonic maps.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 6","pages":"Article 111006"},"PeriodicalIF":1.7,"publicationDate":"2025-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143878679","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 remark on the Hölder regularity of solutions to the complex Hessian equation","authors":"Sławomir Kołodziej ,&nbsp;Ngoc Cuong Nguyen","doi":"10.1016/j.jfa.2025.111005","DOIUrl":"10.1016/j.jfa.2025.111005","url":null,"abstract":"<div><div>We prove that the Dirichlet problem for the complex Hessian equation has the Hölder continuous solution provided it has a subsolution with this property. Compared to the previous result of Benali-Zeriahi and Charabati-Zeriahi we remove the assumption on the finite total mass of the measure on the right hand side.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 6","pages":"Article 111005"},"PeriodicalIF":1.7,"publicationDate":"2025-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143855386","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":"Gagliardo–Nirenberg inequality via a new pointwise estimate","authors":"Karol Leśnik ,&nbsp;Tomáš Roskovec ,&nbsp;Filip Soudský","doi":"10.1016/j.jfa.2025.110996","DOIUrl":"10.1016/j.jfa.2025.110996","url":null,"abstract":"<div><div>We prove a new type of pointwise estimate of the Kałamajska–Mazya–Shaposhnikova type, where sparse averaging operators replace the maximal operator. It allows us to extend the Gagliardo–Nirenberg interpolation inequality to all rearrangement invariant Banach function spaces without any assumptions on their upper Boyd index, i.e. omitting problems caused by unboundedness of maximal operator on spaces close to <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>. In particular, we remove unnecessary assumptions from the Gagliardo–Nirenberg inequality in the setting of Orlicz and Lorentz spaces. The applied method is new in this context and may be seen as a kind of sparse domination technique fitted to the context of rearrangement invariant Banach function spaces.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 7","pages":"Article 110996"},"PeriodicalIF":1.7,"publicationDate":"2025-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143855553","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":"Esscher transform and the central limit theorem","authors":"Sergey G. Bobkov ,&nbsp;Friedrich Götze","doi":"10.1016/j.jfa.2025.110999","DOIUrl":"10.1016/j.jfa.2025.110999","url":null,"abstract":"<div><div>The paper is devoted to the investigation of Esscher's transform on high dimensional Euclidean spaces in the light of its application to the central limit theorem. With this tool, we explore necessary and sufficient conditions of normal approximation for normalized sums of i.i.d. random vectors in terms of the Rényi divergence of infinite order, extending recent one dimensional results.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 5","pages":"Article 110999"},"PeriodicalIF":1.7,"publicationDate":"2025-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143878140","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":"Non-uniqueness of weak solutions for a logarithmically supercritical hyperdissipative Navier-Stokes system","authors":"Marco Romito ,&nbsp;Francesco Triggiano","doi":"10.1016/j.jfa.2025.110989","DOIUrl":"10.1016/j.jfa.2025.110989","url":null,"abstract":"<div><div>Existence of non-unique solutions of finite kinetic energy for the three dimensional Navier-Stokes equations is proved in the slightly supercritical hyper-dissipative setting introduced by Tao <span><span>[20]</span></span>. The result is based on the convex integration techniques of Buckmaster and Vicol <span><span>[3]</span></span>, and extends Luo and Titi <span><span>[16]</span></span> in the slightly supercritical setting. To reach the threshold identified by Tao, we introduce the impulsed Beltrami flows, a variant of the intermittent Beltrami flows of Buckmaster and Vicol.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 4","pages":"Article 110989"},"PeriodicalIF":1.7,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143808225","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":"Connection Laplacian on discrete tori with converging property","authors":"Yong Lin,&nbsp;Shi Wan,&nbsp;Haohang Zhang","doi":"10.1016/j.jfa.2025.110984","DOIUrl":"10.1016/j.jfa.2025.110984","url":null,"abstract":"<div><div>This paper presents a comprehensive analysis of the spectral properties of the connection Laplacian for both real and discrete tori. We introduce novel methods to examine these eigenvalues by employing parallel orthonormal basis in the pullback bundle on universal covering spaces. Our main results reveal that the eigenvalues of the connection Laplacian on a real torus can be expressed in terms of standard Laplacian eigenvalues, with a unique twist encapsulated in the torsion matrix. This connection is further investigated in the context of discrete tori, where we demonstrate similar results.</div><div>A significant portion of the paper is dedicated to exploring the convergence properties of a family of discrete tori towards a real torus. We extend previous findings on the spectrum of the standard Laplacian to include the connection Laplacian, revealing that the rescaled eigenvalues of discrete tori converge to those of the real torus. Furthermore, our analysis of the discrete torus occurs within a broader context, where it is not constrained to being a product of cyclic groups. Additionally, we delve into the theta functions associated with these structures, providing a detailed analysis of their behavior and convergence.</div><div>The paper culminates in a study of the regularized log-determinant of the connection Laplacian and the converging results of it. We derive formulae for both real and discrete tori, emphasizing their dependence on the spectral zeta function and theta functions.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 4","pages":"Article 110984"},"PeriodicalIF":1.7,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143808226","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":"Integral Varadhan formula for non-linear heat flow","authors":"Shin-ichi Ohta ,&nbsp;Kohei Suzuki","doi":"10.1016/j.jfa.2025.110983","DOIUrl":"10.1016/j.jfa.2025.110983","url":null,"abstract":"<div><div>We prove the integral Varadhan short-time formula for non-linear heat flow on measured Finsler manifolds. To the best of the authors' knowledge, this is the first result establishing a Varadhan-type formula for non-linear semigroups. We do not assume the reversibility of the metric, thus the distance function can be asymmetric. In this generality, we reveal that the probabilistic interpretation is well-suited for our formula; the probability that a particle starting from a set <em>A</em> can be found in another set <em>B</em> describes the distance from <em>A</em> to <em>B</em>. One side of the estimates (the upper bound of the probability) is also established in the nonsmooth setting of infinitesimally strictly convex metric measure spaces.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 8","pages":"Article 110983"},"PeriodicalIF":1.7,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143825891","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":"Pseudo-Gevrey smoothing for the passive scalar equations near Couette","authors":"Jacob Bedrossian ,&nbsp;Siming He ,&nbsp;Sameer Iyer ,&nbsp;Fei Wang","doi":"10.1016/j.jfa.2025.110987","DOIUrl":"10.1016/j.jfa.2025.110987","url":null,"abstract":"<div><div>In this article, we study the regularity theory for two linear equations that are important in fluid dynamics: the passive scalar equation for (time-varying) shear flows close to Couette in <span><math><mi>T</mi><mo>×</mo><mo>[</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span> with vanishing diffusivity <span><math><mi>ν</mi><mo>→</mo><mn>0</mn></math></span> and the Poisson equation with right-hand side behaving in similar function spaces to such a passive scalar. The primary motivation for this work is to develop some of the main technical tools required for our treatment of the (nonlinear) 2D Navier-Stokes equations, carried out in our companion work. Both equations are studied with homogeneous Dirichlet conditions (the analogue of a Navier slip-type boundary condition) and the initial condition is taken to be compactly supported away from the walls. We develop smoothing estimates with the following three features:<ul><li><span>(1)</span><span><div>Uniform-in-<em>ν</em> regularity is with respect to <span><math><msub><mrow><mo>∂</mo></mrow><mrow><mi>x</mi></mrow></msub></math></span> and a time-dependent adapted vector-field Γ which approximately commutes with the passive scalar equation (as opposed to ‘flat’ derivatives), and a scaled gradient <span><math><msqrt><mrow><mi>ν</mi></mrow></msqrt><mi>∇</mi></math></span>;</div></span></li><li><span>(2)</span><span><div><span><math><mo>(</mo><msub><mrow><mo>∂</mo></mrow><mrow><mi>x</mi></mrow></msub><mo>,</mo><mi>Γ</mi><mo>)</mo></math></span>-regularity estimates are performed in Gevrey spaces with regularity that depends on the spatial coordinate, <em>y</em> (what we refer to as ‘pseudo-Gevrey’);</div></span></li><li><span>(3)</span><span><div>The regularity of these pseudo-Gevrey spaces degenerates to finite regularity near the center of the channel and hence standard Gevrey product rules and other amenable properties do not hold.</div></span></li></ul> Nonlinear analysis in such a delicate functional setting is one of the key ingredients to our companion paper, <span><span>[5]</span></span>, which proves the full nonlinear asymptotic stability of the Couette flow with slip boundary conditions. The present article introduces new estimates for the associated linear problems in these degenerate pseudo-Gevrey spaces, which is of independent interest.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 7","pages":"Article 110987"},"PeriodicalIF":1.7,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143808609","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}