Journal of Functional Analysis最新文献

{"title":"Second order Sobolev regularity results for the generalized p-parabolic equation","authors":"Yawen Feng ,&nbsp;Mikko Parviainen ,&nbsp;Saara Sarsa","doi":"10.1016/j.jfa.2024.110799","DOIUrl":"10.1016/j.jfa.2024.110799","url":null,"abstract":"<div><div>We study a general class of parabolic equations<span><span><span><math><mrow><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>−</mo><msup><mrow><mo>|</mo><mi>D</mi><mi>u</mi><mo>|</mo></mrow><mrow><mi>γ</mi></mrow></msup><mo>(</mo><mi>Δ</mi><mi>u</mi><mo>+</mo><mo>(</mo><mi>p</mi><mo>−</mo><mn>2</mn><mo>)</mo><msubsup><mrow><mi>Δ</mi></mrow><mrow><mo>∞</mo></mrow><mrow><mi>N</mi></mrow></msubsup><mi>u</mi><mo>)</mo><mo>=</mo><mn>0</mn><mo>,</mo></mrow></math></span></span></span> which can be highly degenerate or singular. This class contains as special cases the standard parabolic <em>p</em>-Laplace equation and the normalized version that arises from stochastic game theory. Utilizing the systematic approach developed in our previous work we establish second order Sobolev regularity together with a priori estimates and improved range of parameters. In addition we derive second order Sobolev estimate for a nonlinear quantity. This quantity contains many useful special cases. As a corollary we also obtain that a viscosity solution has locally <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-integrable Sobolev time derivative.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 5","pages":"Article 110799"},"PeriodicalIF":1.7,"publicationDate":"2024-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143128171","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":"Interior Hölder and Calderón-Zygmund estimates for fully nonlinear equations with natural gradient growth","authors":"Alessandro Goffi","doi":"10.1016/j.jfa.2024.110800","DOIUrl":"10.1016/j.jfa.2024.110800","url":null,"abstract":"<div><div>We establish local Hölder estimates for viscosity solutions of fully nonlinear second order equations with quadratic growth in the gradient and unbounded right-hand side in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>q</mi></mrow></msup></math></span> spaces, for an integrability threshold <em>q</em> guaranteeing the validity of the maximum principle. This is done through a nonlinear Harnack inequality for nonhomogeneous equations driven by a uniformly elliptic Isaacs operator and perturbed by a Hamiltonian term with natural growth in the gradient. As a byproduct, we derive a new Liouville property for entire <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> viscosity solutions of fully nonlinear equations as well as a nonlinear Calderón-Zygmund estimate for strong solutions of such equations.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 5","pages":"Article 110800"},"PeriodicalIF":1.7,"publicationDate":"2024-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143128168","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":"Uncertainty qualification of Vlasov-Poisson-Boltzmann equations in the diffusive scaling","authors":"Ning Jiang ,&nbsp;Xu Zhang","doi":"10.1016/j.jfa.2024.110794","DOIUrl":"10.1016/j.jfa.2024.110794","url":null,"abstract":"<div><div>For the Vlasov-Poisson-Boltzmann equations with random uncertainties from the initial data or collision kernels, we proved the sensitivity analysis and energy estimates uniformly with respect to both the Knudsen number and the random variables in the diffusive scaling using hypocoercivity method developed in <span><span>[6]</span></span>, <span><span>[7]</span></span>, <span><span>[14]</span></span>. As a consequence, we also justified the incompressible Navier-Stokes-Poisson limit with random inputs. In particular, for the first time, we obtain the precise convergence rate <em>without</em> employing any results based on Hilbert expansion (in other words, we don't need any information from the limiting fluid equations <em>a priori</em>). We not only generalized the previous deterministic Navier-Stokes-Fourier-Poisson limits to random initial data case, but also improve the previous uncertainty quantification results to the case where the initial data include both kinetic and fluid parts. This is the first uncertainty qualification (UQ) result for spatially high dimension kinetic equations in diffusive limits containing Navier-Stokes dynamics, and generalizes the previous UQ results which does not contain fluid equations (for example, <span><span>[34]</span></span>).</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 5","pages":"Article 110794"},"PeriodicalIF":1.7,"publicationDate":"2024-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143093237","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 Lavrentiev gap for convex, vectorial integral functionals","authors":"Lukas Koch ,&nbsp;Matthias Ruf ,&nbsp;Mathias Schäffner","doi":"10.1016/j.jfa.2024.110793","DOIUrl":"10.1016/j.jfa.2024.110793","url":null,"abstract":"<div><div>We prove the absence of a Lavrentiev gap for vectorial integral functionals of the form<span><span><span><math><mi>F</mi><mo>:</mo><mi>g</mi><mo>+</mo><msubsup><mrow><mi>W</mi></mrow><mrow><mn>0</mn></mrow><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msubsup><msup><mrow><mo>(</mo><mi>Ω</mi><mo>)</mo></mrow><mrow><mi>m</mi></mrow></msup><mo>→</mo><mo>[</mo><mn>0</mn><mo>,</mo><mo>+</mo><mo>∞</mo><mo>]</mo><mo>,</mo><mspace></mspace><mi>F</mi><mo>(</mo><mi>u</mi><mo>)</mo><mo>=</mo><munder><mo>∫</mo><mrow><mi>Ω</mi></mrow></munder><mi>J</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>D</mi><mi>u</mi><mo>)</mo><mspace></mspace><mi>d</mi><mi>x</mi><mo>,</mo></math></span></span></span> where the boundary datum <span><math><mi>g</mi><mo>:</mo><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>→</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>m</mi></mrow></msup></math></span> is sufficiently regular, <span><math><mi>ξ</mi><mo>↦</mo><mi>J</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>ξ</mi><mo>)</mo></math></span> is convex and lower semicontinuous, satisfies <em>p</em>-growth from below and suitable growth conditions from above. More precisely, if <span><math><mi>p</mi><mo>≤</mo><mi>d</mi><mo>−</mo><mn>1</mn></math></span>, we assume <em>q</em>-growth from above with <span><math><mi>q</mi><mo>≤</mo><mfrac><mrow><mo>(</mo><mi>d</mi><mo>−</mo><mn>1</mn><mo>)</mo><mi>p</mi></mrow><mrow><mi>d</mi><mo>−</mo><mn>1</mn><mo>−</mo><mi>p</mi></mrow></mfrac></math></span>, while for <span><math><mi>p</mi><mo>&gt;</mo><mi>d</mi><mo>−</mo><mn>1</mn></math></span> or <span><math><mi>p</mi><mo>=</mo><mn>1</mn></math></span> if <span><math><mi>d</mi><mo>=</mo><mn>2</mn></math></span>, we require essentially no growth conditions from above and allow for unbounded integrands. Concerning the <em>x</em>-dependence, we impose a well-known local stability estimate that is redundant in the autonomous setting, but in the general non-autonomous case can further restrict the growth assumptions.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 5","pages":"Article 110793"},"PeriodicalIF":1.7,"publicationDate":"2024-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143128211","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":"Elliptic operators in rough sets and the Dirichlet problem with boundary data in Hölder spaces","authors":"Mingming Cao ,&nbsp;Pablo Hidalgo-Palencia ,&nbsp;José María Martell ,&nbsp;Cruz Prisuelos-Arribas ,&nbsp;Zihui Zhao","doi":"10.1016/j.jfa.2024.110801","DOIUrl":"10.1016/j.jfa.2024.110801","url":null,"abstract":"<div><div>In this paper we study the Dirichlet problem for real-valued second order divergence form elliptic operators with boundary data in Hölder spaces. Our context is that of open sets <span><math><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup></math></span>, <span><math><mi>n</mi><mo>≥</mo><mn>2</mn></math></span>, satisfying the capacity density condition, without any further topological assumptions. Our main result states that if Ω is either bounded, or unbounded with unbounded boundary, then the corresponding Dirichlet boundary value problem is well-posed; when Ω is unbounded with bounded boundary, we establish that solutions exist, but they fail to be unique in general. These results are optimal in the sense that solvability of the Dirichlet problem in Hölder spaces is shown to imply the capacity density condition.</div><div>As a consequence of the main result, we present a characterization of the Hölder spaces in terms of the boundary traces of solutions, and obtain well-posedness of several related Dirichlet boundary value problems.</div><div>All the results above are new even for 1-sided chord-arc domains, and can be extended to generalized Hölder spaces associated with a natural class of growth functions.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 5","pages":"Article 110801"},"PeriodicalIF":1.7,"publicationDate":"2024-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143093235","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":"Zeros of L-functions in low-lying intervals and de Branges spaces","authors":"Antonio Pedro Ramos","doi":"10.1016/j.jfa.2024.110788","DOIUrl":"10.1016/j.jfa.2024.110788","url":null,"abstract":"<div><div>We consider a variant of a problem first introduced by Hughes and Rudnick (2003) and generalized by Bernard (2015) concerning conditional bounds for small first zeros in a family of <em>L</em>-functions. Here we seek to estimate the size of the smallest intervals centered at a low-lying height on the critical line for which we can guarantee the existence of a zero in a family of <em>L</em>-functions. This leads us to consider an extremal problem in analysis which we address by applying the framework of de Branges spaces, introduced in this context by Carneiro, Chirre, and Milinovich (2022).</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 5","pages":"Article 110788"},"PeriodicalIF":1.7,"publicationDate":"2024-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143128209","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":"Irreducible approximation of Toeplitz operators","authors":"Hansong Huang ,&nbsp;Yanlin Liu ,&nbsp;Yanyue Shi ,&nbsp;Sen Zhu","doi":"10.1016/j.jfa.2024.110789","DOIUrl":"10.1016/j.jfa.2024.110789","url":null,"abstract":"<div><div>This paper aims to study reducing subspaces of Toeplitz operators via an approximation approach. Halmos proved in 1968 that the set of irreducible operators on a separable Hilbert space is a dense <span><math><msub><mrow><mi>G</mi></mrow><mrow><mi>δ</mi></mrow></msub></math></span> set. We extend Halmos' result to the class <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>C</mi><mo>(</mo><mi>T</mi><mo>)</mo></mrow></msub></math></span> of Toeplitz operators with continuous symbols by proving that those irreducible ones constitute a dense <span><math><msub><mrow><mi>G</mi></mrow><mrow><mi>δ</mi></mrow></msub></math></span> subset of <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>C</mi><mo>(</mo><mi>T</mi><mo>)</mo></mrow></msub></math></span>. In doing so, we give criteria to identify the irreducibility for trigonometric Toeplitz operators and matrices. As an application, we establish Halmos' approximation result for convex subsets of the <span><math><mi>n</mi><mo>×</mo><mi>n</mi></math></span> complex matrix algebra containing at least one irreducible element.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 5","pages":"Article 110789"},"PeriodicalIF":1.7,"publicationDate":"2024-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143093236","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 range of a class of complex Monge-Ampère operators on compact Hermitian manifolds","authors":"Yinji Li ,&nbsp;Zhiwei Wang ,&nbsp;Xiangyu Zhou","doi":"10.1016/j.jfa.2024.110787","DOIUrl":"10.1016/j.jfa.2024.110787","url":null,"abstract":"<div><div>Let <span><math><mo>(</mo><mi>X</mi><mo>,</mo><mi>ω</mi><mo>)</mo></math></span> be a compact Hermitian manifold of complex dimension <em>n</em>. Let <em>β</em> be a smooth real closed <span><math><mo>(</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span> form such that there exists a function <span><math><mi>ρ</mi><mo>∈</mo><mtext>PSH</mtext><mo>(</mo><mi>X</mi><mo>,</mo><mi>β</mi><mo>)</mo><mo>∩</mo><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>(</mo><mi>X</mi><mo>)</mo></math></span>. We study the range of the complex non-pluripolar Monge-Ampère operator <span><math><mo>〈</mo><msup><mrow><mo>(</mo><mi>β</mi><mo>+</mo><mi>d</mi><msup><mrow><mi>d</mi></mrow><mrow><mi>c</mi></mrow></msup><mo>⋅</mo><mo>)</mo></mrow><mrow><mi>n</mi></mrow></msup><mo>〉</mo></math></span> on weighted Monge-Ampère energy classes on <em>X</em>. In particular, when <em>ρ</em> is assumed to be continuous, we give a complete characterization of the range of the complex Monge-Ampère operator on the class <span><math><mi>E</mi><mo>(</mo><mi>X</mi><mo>,</mo><mi>β</mi><mo>)</mo></math></span>, which is the class of all <span><math><mi>φ</mi><mo>∈</mo><mtext>PSH</mtext><mo>(</mo><mi>X</mi><mo>,</mo><mi>β</mi><mo>)</mo></math></span> with full Monge-Ampère mass, i.e. <span><math><msub><mrow><mo>∫</mo></mrow><mrow><mi>X</mi></mrow></msub><mo>〈</mo><msup><mrow><mo>(</mo><mi>β</mi><mo>+</mo><mi>d</mi><msup><mrow><mi>d</mi></mrow><mrow><mi>c</mi></mrow></msup><mi>φ</mi><mo>)</mo></mrow><mrow><mi>n</mi></mrow></msup><mo>〉</mo><mo>=</mo><msub><mrow><mo>∫</mo></mrow><mrow><mi>X</mi></mrow></msub><msup><mrow><mi>β</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 5","pages":"Article 110787"},"PeriodicalIF":1.7,"publicationDate":"2024-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143093265","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":"Piecewise linear and step Fourier multipliers for modulation spaces","authors":"Hans G. Feichtinger ,&nbsp;Ferenc Weisz","doi":"10.1016/j.jfa.2024.110795","DOIUrl":"10.1016/j.jfa.2024.110795","url":null,"abstract":"<div><div>This note significantly extends various earlier results concerning Fourier multipliers of modulation spaces. It combines not so widely known characterizations of pointwise multipliers of Wiener amalgam spaces with novel geometric ideas and a new approach to piecewise linear functions belonging to the Fourier algebra. Thus the paper provides two original types of results.</div><div>On the one hand we establish results for step functions (i.e. piecewise constant, bounded functions), which are multipliers on the modulation spaces <span><math><mo>(</mo><msubsup><mrow><mi>M</mi></mrow><mrow><mi>ω</mi></mrow><mrow><mi>p</mi><mo>,</mo><mi>q</mi></mrow></msubsup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>)</mo><mo>,</mo><msub><mrow><mo>‖</mo><mo>⋅</mo><mo>‖</mo></mrow><mrow><msubsup><mrow><mi>M</mi></mrow><mrow><mi>ω</mi></mrow><mrow><mi>p</mi><mo>,</mo><mi>q</mi></mrow></msubsup></mrow></msub><mo>)</mo></math></span> with <span><math><mn>1</mn><mo>&lt;</mo><mi>p</mi><mo>&lt;</mo><mo>∞</mo></math></span>, fixed. Instead of regular patterns with a discrete subgroup structure we demonstrate that there is a significant freedom in the choice of the domains of constant values. In particular for higher dimensions (i.e., <span><math><mi>d</mi><mo>≥</mo><mn>2</mn></math></span>), this widens the scope of possible multipliers very much. Adding some geometric considerations we show that the step functions, which arise as nearest neighborhood interpolation (using the so-called Voronoi cells) from roughly well-spread sets with bounded values define Fourier multipliers in this range, with uniform control for large families of such sets. Parameterized families of lattices are just simple special cases.</div><div>In the second part of the paper we aim at sufficient conditions for piecewise linear Fourier multipliers, with uniform estimates for the range <span><math><mi>p</mi><mo>∈</mo><mo>[</mo><mn>1</mn><mo>,</mo><mo>∞</mo><mo>]</mo></math></span> (and independent from <em>q</em> and <em>s</em>). These results are based on the control on the Fourier algebra norm of (oblique) triangular functions on <span><math><mi>R</mi></math></span>. This result is of independent interest, as it provides new sufficient conditions for the membership of piecewise linear functions (with irregular nodes) in the modulation space <span><math><msup><mrow><mi>M</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>)</mo></math></span>, also known as the Segal algebra <span><math><msub><mrow><mi>S</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>)</mo></math></span> (see <span><span>[6]</span></span> and <span><span>[25]</span></span>).</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 5","pages":"Article 110795"},"PeriodicalIF":1.7,"publicationDate":"2024-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143128212","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":"Some uniformization problems for a fourth order conformal curvature","authors":"Sanghoon Lee","doi":"10.1016/j.jfa.2024.110791","DOIUrl":"10.1016/j.jfa.2024.110791","url":null,"abstract":"<div><div>In this paper, we establish the existence of conformal deformations that uniformize fourth order curvature on 4-dimensional Riemannian manifolds with positive conformal invariants. Specifically, we prove that any closed, compact Riemannian manifold with positive Yamabe invariant and total <em>Q</em>-curvature can be conformally deformed into a metric with positive scalar curvature and constant <em>Q</em>-curvature. For a Riemannian manifold with umbilic boundary, positive first Yamabe invariant and total <span><math><mo>(</mo><mi>Q</mi><mo>,</mo><mi>T</mi><mo>)</mo></math></span>-curvature, it is possible to deform it into two types of Riemannian manifolds with totally geodesic boundary and positive scalar curvature. The first type satisfies <span><math><mi>Q</mi><mo>≡</mo><mtext>constant</mtext><mo>,</mo><mi>T</mi><mo>≡</mo><mn>0</mn></math></span> while the second type satisfies <span><math><mi>Q</mi><mo>≡</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>≡</mo><mtext>constant</mtext></math></span>.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 5","pages":"Article 110791"},"PeriodicalIF":1.7,"publicationDate":"2024-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143128210","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}