Journal of Functional Analysis最新文献

{"title":"Phase space analysis of finite and infinite dimensional Fresnel integrals","authors":"Sonia Mazzucchi ,&nbsp;Fabio Nicola ,&nbsp;S. Ivan Trapasso","doi":"10.1016/j.jfa.2025.111009","DOIUrl":"10.1016/j.jfa.2025.111009","url":null,"abstract":"<div><div>The full characterization of the class of Fresnel integrable functions is an open problem in functional analysis, with significant applications to mathematical physics (Feynman path integrals) and the analysis of the Schrödinger equation. In finite dimension, we prove the Fresnel integrability of functions in the Sjöstrand class <span><math><msup><mrow><mi>M</mi></mrow><mrow><mo>∞</mo><mo>,</mo><mn>1</mn></mrow></msup></math></span> — a family of continuous and bounded functions, locally enjoying the mild regularity of the Fourier transform of an integrable function. This result broadly extends the current knowledge on the Fresnel integrability of Fourier transforms of finite complex measures, and relies upon ideas and techniques of Gabor wave packet analysis. We also discuss infinite-dimensional extensions of this result. In this connection, we extend and make more concrete the general framework of projective functional extensions introduced by Albeverio and Mazzucchi. In particular, we obtain a concrete example of a continuous linear functional on an infinite-dimensional space beyond the class of Fresnel integrable functions. As an interesting byproduct, we obtain a sharp <span><math><msup><mrow><mi>M</mi></mrow><mrow><mo>∞</mo><mo>,</mo><mn>1</mn></mrow></msup><mo>→</mo><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span> operator norm bound for the free Schrödinger evolution operator.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 8","pages":"Article 111009"},"PeriodicalIF":1.7,"publicationDate":"2025-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143870574","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":"Interior W2,δ type estimates for degenerate fully nonlinear elliptic equations with Ln data","authors":"Sun-Sig Byun ,&nbsp;Hongsoo Kim ,&nbsp;Jehan Oh","doi":"10.1016/j.jfa.2025.111007","DOIUrl":"10.1016/j.jfa.2025.111007","url":null,"abstract":"<div><div>We establish interior <span><math><msup><mrow><mi>W</mi></mrow><mrow><mn>2</mn><mo>,</mo><mi>δ</mi></mrow></msup></math></span> type estimates for a class of degenerate fully nonlinear elliptic equations with <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> data. The main idea of our approach is to slide <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn><mo>,</mo><mi>α</mi></mrow></msup></math></span> cones, instead of paraboloids, vertically to touch the solution, and estimate the contact set in terms of the measure of the vertex set. This shows that the solution has tangent <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn><mo>,</mo><mi>α</mi></mrow></msup></math></span> cones almost everywhere, which leads to the desired Hessian estimates. Accordingly, we are able to develop a kind of counterpart to the estimates for divergent structure quasilinear elliptic problems, as discussed in <span><span>[6]</span></span>, <span><span>[16]</span></span>.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 6","pages":"Article 111007"},"PeriodicalIF":1.7,"publicationDate":"2025-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143874473","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 a class of exact solutions of the incompressible Euler equation in a disk","authors":"Guodong Wang","doi":"10.1016/j.jfa.2025.110998","DOIUrl":"10.1016/j.jfa.2025.110998","url":null,"abstract":"<div><div>We prove a sharp orbital stability result for a class of exact steady solutions, expressed in terms of Bessel functions of the first kind, of the two-dimensional incompressible Euler equation in a disk. A special case of these solutions is the truncated Lamb dipole, whose stream function corresponds to the second eigenfunction of the Dirichlet Laplacian. The proof is achieved by establishing a suitable variational characterization for these solutions via conserved quantities of the Euler equation and employing a compactness argument.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 5","pages":"Article 110998"},"PeriodicalIF":1.7,"publicationDate":"2025-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143854844","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":"Global wellposedness of general nonlinear evolution equations for distributions on the Fourier half space","authors":"Kenji Nakanishi ,&nbsp;Baoxiang Wang","doi":"10.1016/j.jfa.2025.111004","DOIUrl":"10.1016/j.jfa.2025.111004","url":null,"abstract":"<div><div>The Cauchy problem is studied for very general systems of evolution equations, where the time derivative of solution is written by Fourier multipliers in space and analytic nonlinearity, with no other structural requirement. We construct a function space for the Fourier transform embedded in the space of distributions, and establish the global wellposedness with no size restriction. The major restriction on the initial data is that the Fourier transform is supported on the half space, decaying at the boundary in the sense of measure. We also require uniform integrability for the orthogonal directions in the distribution sense, but no other condition. In particular, the initial data may be much more rough than the tempered distributions, and may grow polynomially at the spatial infinity. A simpler argument is also presented for the solutions locally integrable in the frequency. When the Fourier support is slightly more restricted to a conical region, the generality of equations is extremely wide, including those that are even locally illposed in the standard function spaces, such as the backward heat equations, as well as those with infinite derivatives and beyond the natural boundary of the analytic nonlinearity. As more classical examples, our results may be applied to the incompressible and compressible Navier-Stokes and Euler equations, the nonlinear diffusion and wave equations, and so on. In particular, the wellposedness includes uniqueness of very weak solution for those equations, under the Fourier support condition, but with no restriction on regularity or size of solutions. The major drawback of the Fourier support restriction is that the solutions cannot be real valued.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 8","pages":"Article 111004"},"PeriodicalIF":1.7,"publicationDate":"2025-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143870570","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":"Degenerate Poincaré-Sobolev inequalities via fractional integration","authors":"Alejandro Claros","doi":"10.1016/j.jfa.2025.111000","DOIUrl":"10.1016/j.jfa.2025.111000","url":null,"abstract":"<div><div>We present a local weighted estimate for the Riesz potential in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>, which improves the main theorem of Alberico et al. (2009) <span><span>[2]</span></span> in several ways. As a consequence, we derive weighted Poincaré-Sobolev inequalities with sharp dependence on the constants. We answer positively to a conjecture proposed by Pérez and Rela (2019) <span><span>[36]</span></span> related to the sharp exponent in the <span><math><msub><mrow><mi>A</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> constant in the <span><math><mo>(</mo><msup><mrow><mi>p</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>,</mo><mi>p</mi><mo>)</mo></math></span> Poincaré-Sobolev inequality with <span><math><msub><mrow><mi>A</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> weights. Our approach is versatile enough to prove Poincaré-Sobolev inequalities for high-order derivatives and fractional Poincaré-Sobolev inequalities with the BBM extra gain factor <span><math><msup><mrow><mo>(</mo><mn>1</mn><mo>−</mo><mi>δ</mi><mo>)</mo></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mi>p</mi></mrow></mfrac></mrow></msup></math></span>. In particular, we improve one of the main results from Hurri-Syrjänen et al. (2023) <span><span>[24]</span></span>.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 6","pages":"Article 111000"},"PeriodicalIF":1.7,"publicationDate":"2025-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143878677","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 sharp higher order Sobolev inequality on Riemannian manifolds","authors":"Samuel Zeitler","doi":"10.1016/j.jfa.2025.111001","DOIUrl":"10.1016/j.jfa.2025.111001","url":null,"abstract":"&lt;div&gt;&lt;div&gt;Let &lt;span&gt;&lt;math&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; be integers such that &lt;span&gt;&lt;math&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; and let &lt;span&gt;&lt;math&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; be a closed &lt;em&gt;n&lt;/em&gt;-dimensional Riemannian manifold. We prove there exists some &lt;span&gt;&lt;math&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; depending only on &lt;span&gt;&lt;math&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;, &lt;em&gt;m&lt;/em&gt;, and &lt;em&gt;n&lt;/em&gt; such that for all &lt;span&gt;&lt;math&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;,&lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mo&gt;‖&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;‖&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;#&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mi&gt;K&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;munder&gt;&lt;mo&gt;∫&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/mrow&gt;&lt;/munder&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mo&gt;‖&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;‖&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&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;&lt;/span&gt;&lt;/span&gt; where &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;#&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;mi&gt;K&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; is the square of the best constant for the embedding &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;W&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;(&lt;/mo&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;mo&gt;)&lt;/mo&gt;&lt;mo&gt;⊂&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;#&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;(&lt;/mo&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;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; is the Sobolev space consisting of functions on &lt;em&gt;M&lt;/em&gt; with &lt;em&gt;m&lt;/em&gt; weak derivatives in &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;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;, and &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; if &lt;em&gt;m&lt;/em&gt; is odd. This","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 6","pages":"Article 111001"},"PeriodicalIF":1.7,"publicationDate":"2025-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143864177","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 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}