Journal of Functional Analysis最新文献

{"title":"Sampling discretization in Orlicz spaces","authors":"Egor Kosov ,&nbsp;Sergey Tikhonov","doi":"10.1016/j.jfa.2025.110971","DOIUrl":"10.1016/j.jfa.2025.110971","url":null,"abstract":"<div><div>We obtain new sampling discretization results in Orlicz norms on finite dimensional spaces. As applications, we study sampling recovery problems, where the error of the recovery process is calculated with respect to different Orlicz norms. In particular, we are interested in the recovery by linear and nonlinear methods in the norms close to <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 7","pages":"Article 110971"},"PeriodicalIF":1.7,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143815319","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":"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":"Compactness criteria in quasi-Banach symmetric operator spaces associated with a non-commutative torus","authors":"J. Huang ,&nbsp;Y. Nessipbayev ,&nbsp;F. Sukochev ,&nbsp;D. Zanin","doi":"10.1016/j.jfa.2025.110946","DOIUrl":"10.1016/j.jfa.2025.110946","url":null,"abstract":"<div><div>We present two new compactness criteria in non-commutative quasi-Banach symmetric spaces associated to a finite von Neumann algebra, with focus on the non-commutative torus. The first result is novel, even in the commutative setting; while the second resembles the Kolmogorov–Riesz compactness theorem (see <span><span>Theorem 4.1</span></span>, <span><span>Theorem 5.7</span></span>, respectively). The work contributes to understanding a conjecture of Brudnyi, adapted here for the non-commutative torus.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 5","pages":"Article 110946"},"PeriodicalIF":1.7,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143748537","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":"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":"Quenched large deviation principles for random projections of ℓpn balls","authors":"Patrick Lopatto,&nbsp;Kavita Ramanan,&nbsp;Xiaoyu Xie","doi":"10.1016/j.jfa.2025.110937","DOIUrl":"10.1016/j.jfa.2025.110937","url":null,"abstract":"&lt;div&gt;&lt;div&gt;Let &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; be a sequence of positive integers growing to infinity at a sublinear rate, &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;mo&gt;∞&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; as &lt;span&gt;&lt;math&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;mo&gt;∞&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;. Given a sequence of &lt;em&gt;n&lt;/em&gt;-dimensional random vectors &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;Y&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; belonging to a certain class, which includes uniform distributions on suitably scaled &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;ℓ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/math&gt;&lt;/span&gt;-balls or &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;ℓ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/math&gt;&lt;/span&gt;-spheres, &lt;span&gt;&lt;math&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;, and product distributions with sub-Gaussian marginals, we study the large deviations behavior of the corresponding sequence of &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;-dimensional orthogonal projections &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;Y&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; as &lt;span&gt;&lt;math&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;mo&gt;∞&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;, where &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; is an &lt;span&gt;&lt;math&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;×&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;-dimensional projection matrix lying in the Stiefel manifold of orthonormal &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;-frames in &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt;. For almost every sequence of projection matrices, we establish a large deviation principle (LDP) for the corresponding sequence of projections, with a fairly explicit rate function that does not depend on the sequence of projection matrices. As corollaries, we also obtain quenched LDPs for sequences of &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ℓ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;-norms and &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ℓ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;∞&lt;/mo&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;-norms of the coordinates of the projections. Past work on LDPs for projections with growing dimension has mainly focused on ","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 6","pages":"Article 110937"},"PeriodicalIF":1.7,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143799252","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":"On the lack of selection for the transport equation over a dense set of vector fields","authors":"Jules Pitcho","doi":"10.1016/j.jfa.2025.110942","DOIUrl":"10.1016/j.jfa.2025.110942","url":null,"abstract":"<div><div>We construct a set of bounded vector fields dense in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>2</mn><mo>)</mo><mo>;</mo><msubsup><mrow><mi>W</mi></mrow><mrow><mi>l</mi><mi>o</mi><mi>c</mi></mrow><mrow><mi>s</mi><mo>,</mo><mi>p</mi></mrow></msubsup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>;</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>)</mo><mo>)</mo></math></span> for <span><math><mn>1</mn><mo>≤</mo><mi>p</mi><mo>&lt;</mo><mo>+</mo><mo>∞</mo></math></span> and <span><math><mn>0</mn><mo>≤</mo><mi>s</mi><mo>&lt;</mo><mn>1</mn></math></span> with <span><math><mi>p</mi><mo>&lt;</mo><mn>1</mn><mo>/</mo><mi>s</mi></math></span> for which smooth regularisation of the vector field does not give a selection criterion for the continuity equation, thereby showing that the two examples constructed in <span><span>[10]</span></span>, <span><span>[12]</span></span> are generic.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 6","pages":"Article 110942"},"PeriodicalIF":1.7,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143786172","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":"Classical solutions to the thin-film equation with general mobility in the perfect-wetting regime","authors":"Manuel V. Gnann,&nbsp;Anouk C. Wisse","doi":"10.1016/j.jfa.2025.110941","DOIUrl":"10.1016/j.jfa.2025.110941","url":null,"abstract":"&lt;div&gt;&lt;div&gt;We prove well-posedness, partial regularity, and stability of the thin-film equation &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; with general mobility &lt;span&gt;&lt;math&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; and mobility exponent &lt;span&gt;&lt;math&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;∪&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; in the regime of perfect wetting (zero contact angle). After a suitable coordinate transformation to fix the free boundary (the contact line where liquid, air, and solid coalesce), the thin-film equation is rewritten as an abstract Cauchy problem and we obtain maximal &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/math&gt;&lt;/span&gt;-regularity for the linearized evolution. Partial regularity close to the free boundary is obtained by studying the elliptic regularity of the spatial part of the linearization. This yields solutions that are non-smooth in the distance to the free boundary, in line with previous findings for source-type self-similar solutions. In a scaling-wise quasi-minimal norm for the initial data, we obtain a well-posedness and asymptotic stability result for perturbations of traveling waves. The novelty of this work lies in the usage of &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt;-estimates in time, where &lt;span&gt;&lt;math&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mo&gt;∞&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;, while the existing literature mostly deals with &lt;span&gt;&lt;math&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; at least for nonlinear mobilities. This turns out to be essential to obtain for the first time a well-posedness result in the perfect-wetting regime for all physical nonlinear slip conditions except for a strongly degenerate case at &lt;span&gt;&lt;math&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/math&gt;&lt;/span&gt; and the well-understood Greenspan-slip case &lt;span&gt;&lt;math&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;. Furthermore, compared to &lt;span&gt;&lt;span&gt;[36]&lt;/span&gt;&lt;/span&gt; by Giacomelli, the first author of this paper, Knüpfer, and Otto, where a PDE approach yields &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/math&gt;&lt;/span&gt;-estimates, well-posedness, and stability for &lt;span&gt;&lt;math&gt;&lt;mn&gt;1.8384&lt;/mn&gt;&lt;mo&gt;≈&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;17&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;15&lt;/mn&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;msqrt&gt;&lt;mrow&gt;&lt;mn&gt;21&lt;/mn&gt;&lt;/mrow&gt;&lt;/msqrt&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mi","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 8","pages":"Article 110941"},"PeriodicalIF":1.7,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143837981","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}