{"title":"关于带反射的奇异积分算子","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":"{\"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}","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}
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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