{"title":"On singular integral operators with reflection","authors":"A. G. Kamalyan","doi":"10.1007/s43036-024-00416-8","DOIUrl":null,"url":null,"abstract":"<div><p>The aim of the present paper is the investigation of matrix singular integral operators with reflection in Lebesgue spaces on the real line with Muckenhoupt weights. It is proved that these operators are matrix coupled with matrix Toeplitz operators. As a corollary, a criterion for the Fredholmness of such operators with piecewise continuous coefficients is obtained. Singular integral operators with flip and Toeplitz plus Hankel operators are also considered.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Operator Theory","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s43036-024-00416-8","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
The aim of the present paper is the investigation of matrix singular integral operators with reflection in Lebesgue spaces on the real line with Muckenhoupt weights. It is proved that these operators are matrix coupled with matrix Toeplitz operators. As a corollary, a criterion for the Fredholmness of such operators with piecewise continuous coefficients is obtained. Singular integral operators with flip and Toeplitz plus Hankel operators are also considered.
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