Corresponding to harmonic Bergman space, in this paper we study Toeplitz operators of pluriharmonic Hardy space. We find the properties of Toeplitz operators on h 2 ( D 2 ) are greatly different from the classical Hardy space, Bergman space and harmonic Bergman space. For example, two analytic Toeplitz operators maybe not semi-commute or commute. Even if it is semi-commute, neither of both symbols is constant; Even if it is commute, their symbols’ nontrivial linear combination may be not constant. We obtain the necessary and sufficient condition of two analytic Toeplitz operators semi-commute and commute on h 2 ( D 2 ).
{"title":"双圆盘上Hardy-Toeplitz算子的几个问题","authors":"Xuanhao Ding, Zhangyi Wang, Yongning Li","doi":"10.1360/012012-292","DOIUrl":"https://doi.org/10.1360/012012-292","url":null,"abstract":"Corresponding to harmonic Bergman space, in this paper we study Toeplitz operators of pluriharmonic Hardy space. We find the properties of Toeplitz operators on h 2 ( D 2 ) are greatly different from the classical Hardy space, Bergman space and harmonic Bergman space. For example, two analytic Toeplitz operators maybe not semi-commute or commute. Even if it is semi-commute, neither of both symbols is constant; Even if it is commute, their symbols’ nontrivial linear combination may be not constant. We obtain the necessary and sufficient condition of two analytic Toeplitz operators semi-commute and commute on h 2 ( D 2 ).","PeriodicalId":36277,"journal":{"name":"Scientia Sinica Mathematica","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45923072","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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