{"title":"Pointwise convergence for the heat equation on tori Tn and waveguide manifold Tn×Rm","authors":"Divyang G. Bhimani, Rupak K. Dalai","doi":"10.1016/j.jmaa.2025.129389","DOIUrl":null,"url":null,"abstract":"<div><div>We completely characterize the weighted Lebesgue spaces on the torus <span><math><msup><mrow><mi>T</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> and waveguide manifold <span><math><msup><mrow><mi>T</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>×</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>m</mi></mrow></msup></math></span> for which the solutions of the heat equation converge pointwise (as time tends to zero) to the initial data. In the process, we also characterize the weighted Lebesgue spaces for the boundedness of maximal operators on the torus and waveguide manifold, which may be of independent interest.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"548 1","pages":"Article 129389"},"PeriodicalIF":1.2000,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Analysis and Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022247X25001702","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We completely characterize the weighted Lebesgue spaces on the torus and waveguide manifold for which the solutions of the heat equation converge pointwise (as time tends to zero) to the initial data. In the process, we also characterize the weighted Lebesgue spaces for the boundedness of maximal operators on the torus and waveguide manifold, which may be of independent interest.
期刊介绍:
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