Journal of Functional Analysis最新文献

{"title":"Viscosity solution to complex Hessian equations on compact Hermitian manifolds","authors":"Jingrui Cheng,&nbsp;Yulun Xu","doi":"10.1016/j.jfa.2025.110936","DOIUrl":"10.1016/j.jfa.2025.110936","url":null,"abstract":"<div><div>We prove the existence of viscosity solutions to complex Hessian equations on a compact Hermitian manifold that satisfy a determinant domination condition. This viscosity solution is shown to be unique when the right hand is strictly monotone increasing in terms of the solution. When the right hand side does not depend on the solution, we reduces it to the strict monotonicity of the solvability constant.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 5","pages":"Article 110936"},"PeriodicalIF":1.7,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738471","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":"Two new constant rank theorems","authors":"Qinfeng Li,&nbsp;Lu Xu","doi":"10.1016/j.jfa.2025.110935","DOIUrl":"10.1016/j.jfa.2025.110935","url":null,"abstract":"<div><div>Motivated from one-dimensional rigidity results of entire solutions to Liouville equation, we consider the semilinear equation<span><span><span>(0.1)</span><span><math><mrow><mi>Δ</mi><mi>u</mi><mo>=</mo><mi>G</mi><mo>(</mo><mi>u</mi><mo>)</mo><mspace></mspace><mrow><mtext>in </mtext><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></mrow><mo>,</mo></mrow></math></span></span></span>where <span><math><mi>G</mi><mo>&gt;</mo><mn>0</mn><mo>,</mo><msup><mrow><mi>G</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>&lt;</mo><mn>0</mn></math></span> and <span><math><mi>G</mi><msup><mrow><mi>G</mi></mrow><mrow><mo>″</mo></mrow></msup><mo>≤</mo><mi>A</mi><msup><mrow><mo>(</mo><msup><mrow><mi>G</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></math></span>, with <span><math><mi>A</mi><mo>&gt;</mo><mn>0</mn></math></span>. Let <em>u</em> be a smooth convex solution to <span><span>(0.1)</span></span> and <span><math><msub><mrow><mi>σ</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>(</mo><msup><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>u</mi><mo>)</mo></math></span> be the <em>k</em>-th elementary symmetric polynomial with respect to <span><math><msup><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>u</mi></math></span>. Under the above conditions, we prove the following two new constant rank theorems:<ul><li><span>(1)</span><span><div>If <span><math><msub><mrow><mi>σ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><msup><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>u</mi><mo>)</mo></math></span> has a local minimum, then <span><math><msup><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>u</mi></math></span> has constant rank 1 for <span><math><mi>A</mi><mo>≤</mo><mn>2</mn></math></span>.</div></span></li><li><span>(2)</span><span><div>If <span><math><msub><mrow><mi>σ</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><msup><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>u</mi><mo>)</mo></math></span> has a local minimum, then <span><math><msub><mrow><mi>σ</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><msup><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>u</mi><mo>)</mo></math></span> is always zero and <span><math><msup><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>u</mi></math></span> must have constant rank <span><math><mi>r</mi><mo>≤</mo><mi>n</mi><mo>−</mo><mn>1</mn></math></span> in the domain for <span><math><mi>A</mi><mo>≤</mo><mfrac><mrow><mi>n</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></mfrac></math></span>.</div></span></li></ul></div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 4","pages":"Article 110935"},"PeriodicalIF":1.7,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143737989","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":"Commutator estimates for Haar shifts with general measures","authors":"Tainara Borges ,&nbsp;José M. Conde Alonso ,&nbsp;Jill Pipher ,&nbsp;Nathan A. Wagner","doi":"10.1016/j.jfa.2025.110945","DOIUrl":"10.1016/j.jfa.2025.110945","url":null,"abstract":"<div><div>We study <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><mi>μ</mi><mo>)</mo></math></span> estimates for the commutator <span><math><mo>[</mo><mi>H</mi><mo>,</mo><mi>b</mi><mo>]</mo></math></span>, where the operator <span><math><mi>H</mi></math></span> is a dyadic model of the classical Hilbert transform introduced in <span><span>[9]</span></span>, <span><span>[10]</span></span> and is adapted to a non-doubling Borel measure <em>μ</em> satisfying a dyadic regularity condition which is necessary for <span><math><mi>H</mi></math></span> to be bounded on <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><mi>μ</mi><mo>)</mo></math></span>. We show that <span><math><msub><mrow><mo>‖</mo><mo>[</mo><mi>H</mi><mo>,</mo><mi>b</mi><mo>]</mo><mo>‖</mo></mrow><mrow><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><mi>μ</mi><mo>)</mo><mo>→</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><mi>μ</mi><mo>)</mo></mrow></msub><mo>≲</mo><msub><mrow><mo>‖</mo><mi>b</mi><mo>‖</mo></mrow><mrow><mrow><mi>BMO</mi></mrow><mo>(</mo><mi>μ</mi><mo>)</mo></mrow></msub></math></span>, but to <em>characterize</em> martingale BMO requires additional commutator information. We prove weighted inequalities for <span><math><mo>[</mo><mi>H</mi><mo>,</mo><mi>b</mi><mo>]</mo></math></span> together with a version of the John-Nirenberg inequality adapted to appropriate weight classes <span><math><msub><mrow><mover><mrow><mi>A</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></mrow><mrow><mi>p</mi></mrow></msub></math></span> that we define for our non-homogeneous setting. This requires establishing reverse Hölder inequalities for these new weight classes. Finally, we revisit the appropriate class of nonhomogeneous measures <em>μ</em> for the study of different types of Haar shift operators.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 5","pages":"Article 110945"},"PeriodicalIF":1.7,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143705772","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":"Quantum trajectories. Spectral gap, quasi-compactness & limit theorems","authors":"Tristan Benoist,&nbsp;Arnaud Hautecœur,&nbsp;Clément Pellegrini","doi":"10.1016/j.jfa.2025.110932","DOIUrl":"10.1016/j.jfa.2025.110932","url":null,"abstract":"<div><div>Quantum trajectories are Markov processes modeling the evolution of a quantum system subjected to repeated independent measurements. Inspired by the theory of random products of matrices, it has been shown that these Markov processes admit a unique invariant measure under a purification and irreducibility assumptions. This paper is devoted to the spectral study of the underlying Markov operator. Using Quasi-compactness, it is shown that this operator admits a spectral gap and the peripheral spectrum is described in a precise manner. Next two perturbations of this operator are studied. This allows to derive limit theorems (Central Limit Theorem, Berry-Esseen bounds and Large Deviation Principle) for the empirical mean of functions of the Markov chain as well as the Lyapounov exponent of the underlying random dynamical system.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 5","pages":"Article 110932"},"PeriodicalIF":1.7,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738468","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 weighted decoupling inequality and its application to the maximal Bochner-Riesz problem","authors":"Shengwen Gan ,&nbsp;Shukun Wu","doi":"10.1016/j.jfa.2025.110943","DOIUrl":"10.1016/j.jfa.2025.110943","url":null,"abstract":"<div><div>We prove some weighted <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><msup><mrow><mi>ℓ</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>-decoupling estimates when <span><math><mi>p</mi><mo>=</mo><mn>2</mn><mi>n</mi><mo>/</mo><mo>(</mo><mi>n</mi><mo>−</mo><mn>1</mn><mo>)</mo></math></span>. As an application, we give a result beyond the real interpolation exponents for the maximal Bochner-Riesz operator in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>. We also make an improvement in the planar case.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 3","pages":"Article 110943"},"PeriodicalIF":1.7,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143685943","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 some intrinsic differentiability properties for absolutely continuous functions between Carnot groups and the area formula","authors":"Andrea Pinamonti,&nbsp;Francesco Serra Cassano,&nbsp;Kilian Zambanini","doi":"10.1016/j.jfa.2025.110948","DOIUrl":"10.1016/j.jfa.2025.110948","url":null,"abstract":"<div><div>We discuss <em>Q</em>-absolutely continuous functions between Carnot groups, following Malý's definition for maps of several variables (<span><span>[43]</span></span>). Such maps enjoy nice regularity properties, like continuity, Pansu differentiability a.e., weak differentiability and an area formula. Furthermore, we extend Stein's result concerning the sharp condition for continuity and differentiability a.e. of a Sobolev map in terms of the integrability of the weak gradient: more precisely, we prove that a Sobolev map between Carnot groups with horizontal gradient of its sections uniformly bounded in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>Q</mi><mo>,</mo><mn>1</mn></mrow></msup></math></span> admits a representative which is <em>Q</em>-absolutely continuous.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 3","pages":"Article 110948"},"PeriodicalIF":1.7,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143685944","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":"Isoperimetric problem and structure at infinity on Alexandrov spaces with nonnegative curvature","authors":"Gioacchino Antonelli ,&nbsp;Marco Pozzetta","doi":"10.1016/j.jfa.2025.110940","DOIUrl":"10.1016/j.jfa.2025.110940","url":null,"abstract":"<div><div>In this paper we consider nonnegatively curved finite dimensional Alexandrov spaces with a non-collapsing condition, i.e., such that unit balls have volumes uniformly bounded from below away from zero. We study the relation between the isoperimetric profile, the existence of isoperimetric sets, and the asymptotic structure at infinity of such spaces.</div><div>In this setting, we prove that the following conditions are equivalent: the space has linear volume growth; it is Gromov–Hausdorff asymptotic to one cylinder at infinity; it has uniformly bounded isoperimetric profile; the entire space is a tubular neighborhood of either a line or a ray.</div><div>Moreover, on a space satisfying any of the previous conditions, we prove existence of isoperimetric sets for sufficiently large volumes, and we characterize the geometric rigidity at the level of the isoperimetric profile.</div><div>Specializing our study to the 2-dimensional case, we prove that unit balls have always volumes uniformly bounded from below away from zero, and we prove existence of isoperimetric sets for every volume, characterizing also their topology when the space has no boundary.</div><div>The proofs exploit a variational approach, and in particular apply to Riemannian manifolds with nonnegative sectional curvature and to Euclidean convex bodies. Up to the authors' knowledge, most of the results are new even in these smooth cases.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 4","pages":"Article 110940"},"PeriodicalIF":1.7,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143737988","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":"Diagonals of self-adjoint operators I: Compact operators","authors":"Marcin Bownik ,&nbsp;John Jasper","doi":"10.1016/j.jfa.2025.110939","DOIUrl":"10.1016/j.jfa.2025.110939","url":null,"abstract":"<div><div>Given a self-adjoint operator <em>T</em> on a separable infinite-dimensional Hilbert space we study the problem of characterizing the set <span><math><mi>D</mi><mo>(</mo><mi>T</mi><mo>)</mo></math></span> of all possible diagonals of <em>T</em>. For compact operators <em>T</em>, we give a complete characterization of diagonals modulo the kernel of <em>T</em>. That is, we characterize <span><math><mi>D</mi><mo>(</mo><mi>T</mi><mo>)</mo></math></span> for the class of operators sharing the same nonzero eigenvalues (with multiplicities) as <em>T</em>. Moreover, we determine <span><math><mi>D</mi><mo>(</mo><mi>T</mi><mo>)</mo></math></span> for a fixed compact operator <em>T</em>, modulo the kernel problem for positive compact operators with finite-dimensional kernel.</div><div>Our results generalize a characterization of diagonals of trace class positive operators by Arveson and Kadison <span><span>[5]</span></span> and diagonals of compact positive operators by Kaftal and Weiss <span><span>[24]</span></span> and Loreaux and Weiss <span><span>[28]</span></span>. The proof uses the technique of diagonal-to-diagonal results, which was pioneered in the earlier joint work of the authors with Siudeja <span><span>[12]</span></span>.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 5","pages":"Article 110939"},"PeriodicalIF":1.7,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738470","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":"Murray–von Neumann dimension for strictly semifinite weights","authors":"Aldo Garcia Guinto,&nbsp;Matthew Lorentz,&nbsp;Brent Nelson","doi":"10.1016/j.jfa.2025.110938","DOIUrl":"10.1016/j.jfa.2025.110938","url":null,"abstract":"<div><div>Given a von Neumann algebra <em>M</em> equipped with a faithful normal strictly semifinite weight <em>φ</em>, we develop a notion of Murray–von Neumann dimension over <span><math><mo>(</mo><mi>M</mi><mo>,</mo><mi>φ</mi><mo>)</mo></math></span> that is defined for modules over the basic construction associated to the inclusion <span><math><msup><mrow><mi>M</mi></mrow><mrow><mi>φ</mi></mrow></msup><mo>⊂</mo><mi>M</mi></math></span>. For <span><math><mi>φ</mi><mo>=</mo><mi>τ</mi></math></span> a faithful normal tracial state, this recovers the usual Murray–von Neumann dimension for finite von Neumann algebras. If <em>M</em> is either a type <span><math><msub><mrow><mi>III</mi></mrow><mrow><mi>λ</mi></mrow></msub></math></span> factor with <span><math><mn>0</mn><mo>&lt;</mo><mi>λ</mi><mo>&lt;</mo><mn>1</mn></math></span> or a full type <span><math><msub><mrow><mi>III</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> factor with <span><math><mi>Sd</mi><mo>(</mo><mi>M</mi><mo>)</mo><mo>≠</mo><mi>R</mi></math></span>, then amongst extremal almost periodic weights the dimension function depends on <em>φ</em> only up to scaling. As an application, we show that if an inclusion of diffuse factors with separable preduals <span><math><mi>N</mi><mo>⊂</mo><mi>M</mi></math></span> is with expectation <span><math><mi>E</mi></math></span> and admits a compatible extremal almost periodic state <em>φ</em>, then this dimension quantity bounds the index <span><math><mi>Ind</mi><mspace></mspace><mi>E</mi></math></span>, and in fact equals it when the modular operators <span><math><msub><mrow><mi>Δ</mi></mrow><mrow><mi>φ</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>Δ</mi></mrow><mrow><mi>φ</mi><msub><mrow><mo>|</mo></mrow><mrow><mi>N</mi></mrow></msub></mrow></msub></math></span> have the same point spectrum. In the pursuit of this result, we also show such inclusions always admit Pimsner–Popa orthogonal bases.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 5","pages":"Article 110938"},"PeriodicalIF":1.7,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738469","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 concept of mapped coercivity for nonlinear operators in Banach spaces","authors":"Roland Becker ,&nbsp;Malte Braack","doi":"10.1016/j.jfa.2025.110893","DOIUrl":"10.1016/j.jfa.2025.110893","url":null,"abstract":"<div><div>We provide a concise proof of existence of the solutions to nonlinear operator equations in separable Banach spaces, without assuming the operator to be monotone. Instead, our main hypotheses consist of a continuity assumption and a mapped coercivity property, which is a generalization of the usual coercivity property for nonlinear operators. In the case of linear operators, we recover the traditional inf-sup condition. To illustrate the applicability of this general concept, we apply it to semi-linear elliptic problems and the Navier-Stokes equations.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 3","pages":"Article 110893"},"PeriodicalIF":1.7,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143620534","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}