{"title":"Noncommutative maximal operators with rough kernels","authors":"Xudong Lai","doi":"10.2140/apde.2024.17.1439","DOIUrl":null,"url":null,"abstract":"<p>This paper is devoted to the study of noncommutative maximal operators with rough kernels. More precisely, we prove the weak-type <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo stretchy=\"false\">(</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo stretchy=\"false\">)</mo></math> boundedness for noncommutative maximal operators with rough kernels. The proof of the weak-type <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo stretchy=\"false\">(</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo stretchy=\"false\">)</mo></math> estimate is based on the noncommutative Calderón–Zygmund decomposition. To deal with the rough kernel, we use the microlocal decomposition in the proofs of both the bad and good functions. </p>","PeriodicalId":49277,"journal":{"name":"Analysis & PDE","volume":"29 1","pages":""},"PeriodicalIF":1.8000,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Analysis & PDE","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2140/apde.2024.17.1439","RegionNum":1,"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
This paper is devoted to the study of noncommutative maximal operators with rough kernels. More precisely, we prove the weak-type boundedness for noncommutative maximal operators with rough kernels. The proof of the weak-type estimate is based on the noncommutative Calderón–Zygmund decomposition. To deal with the rough kernel, we use the microlocal decomposition in the proofs of both the bad and good functions.
期刊介绍：
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