{"title":"Bergman空间中Toeplitz算子的紧性","authors":"J. Taskinen, J. Virtanen","doi":"10.7169/FACM/1727","DOIUrl":null,"url":null,"abstract":"In this paper we consider Toepliz operators with (locally) integrable symbols acting on Bergman spaces Ap (1<p<∞) of the open unit disc of the complex plane. We give a characterization of compact Toeplitz operators with symbols in L1 under a mild additional condition. Our result is new even in the Hilbert space setting of A2, where it extends the well-known characterization of compact Toeplitz operators with bounded symbols by Stroethoff and Zheng.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.7169/FACM/1727","citationCount":"2","resultStr":"{\"title\":\"On compactness of Toeplitz operators in Bergman spaces\",\"authors\":\"J. Taskinen, J. Virtanen\",\"doi\":\"10.7169/FACM/1727\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we consider Toepliz operators with (locally) integrable symbols acting on Bergman spaces Ap (1<p<∞) of the open unit disc of the complex plane. We give a characterization of compact Toeplitz operators with symbols in L1 under a mild additional condition. Our result is new even in the Hilbert space setting of A2, where it extends the well-known characterization of compact Toeplitz operators with bounded symbols by Stroethoff and Zheng.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2018-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.7169/FACM/1727\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.7169/FACM/1727\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.7169/FACM/1727","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}