{"title":"Weighted Kato–Ponce inequalities for multiple factors","authors":"Sean Douglas, Loukas Grafakos","doi":"10.1002/mana.202300443","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we establish a weighted Kato–Ponce inequality for <span></span><math>\n <semantics>\n <mi>m</mi>\n <annotation>$m$</annotation>\n </semantics></math> factors in the endpoint case. Furthermore, we extend the validity of the Kato–Ponce inequality from the class of Schwartz functions to the broader class of functions living in a (weighted) fractional Sobolev space.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 10","pages":"3700-3722"},"PeriodicalIF":0.8000,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematische Nachrichten","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/mana.202300443","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we establish a weighted Kato–Ponce inequality for factors in the endpoint case. Furthermore, we extend the validity of the Kato–Ponce inequality from the class of Schwartz functions to the broader class of functions living in a (weighted) fractional Sobolev space.
期刊介绍：
Mathematische Nachrichten - Mathematical News publishes original papers on new results and methods that hold prospect for substantial progress in mathematics and its applications. All branches of analysis, algebra, number theory, geometry and topology, flow mechanics and theoretical aspects of stochastics are given special emphasis. Mathematische Nachrichten is indexed/abstracted in Current Contents/Physical, Chemical and Earth Sciences; Mathematical Review; Zentralblatt für Mathematik; Math Database on STN International, INSPEC; Science Citation Index
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