{"title":"单位球上全纯函数BESOV空间上的算子","authors":"A. Harutyunyan, W. Lusky","doi":"10.46991/pysu:a/2017.51.2.139","DOIUrl":null,"url":null,"abstract":"In the present paper we consider the Toeplitz-$T_{\\bar{h}}^{ \\alpha}$ and differentiation-$D^\\delta $ operators on the Besov spaces $B_p(\\beta)$ for all $0< p<\\infty.$ We show that $T_{\\bar{h}}^{ \\alpha}: B_p(\\beta)\\rightarrow B_p(\\beta)$ for $\\bar h\\in H^\\infty(B^n)$ and $D^\\delta :B_p(\\beta)\\rightarrow B_p(\\widetilde\\beta)$, where $\\widetilde\\beta=\\beta +p\\delta .$","PeriodicalId":21146,"journal":{"name":"Proceedings of the YSU A: Physical and Mathematical Sciences","volume":"39 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2017-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"OPERATORS ON THE BESOV SPACES OF HOLOMORPHIC FUNCTIONS ON THE UNIT BALL IN $\\\\mathbb{C}^n$\",\"authors\":\"A. Harutyunyan, W. Lusky\",\"doi\":\"10.46991/pysu:a/2017.51.2.139\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In the present paper we consider the Toeplitz-$T_{\\\\bar{h}}^{ \\\\alpha}$ and differentiation-$D^\\\\delta $ operators on the Besov spaces $B_p(\\\\beta)$ for all $0< p<\\\\infty.$ We show that $T_{\\\\bar{h}}^{ \\\\alpha}: B_p(\\\\beta)\\\\rightarrow B_p(\\\\beta)$ for $\\\\bar h\\\\in H^\\\\infty(B^n)$ and $D^\\\\delta :B_p(\\\\beta)\\\\rightarrow B_p(\\\\widetilde\\\\beta)$, where $\\\\widetilde\\\\beta=\\\\beta +p\\\\delta .$\",\"PeriodicalId\":21146,\"journal\":{\"name\":\"Proceedings of the YSU A: Physical and Mathematical Sciences\",\"volume\":\"39 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2017-08-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the YSU A: Physical and Mathematical Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.46991/pysu:a/2017.51.2.139\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the YSU A: Physical and Mathematical Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.46991/pysu:a/2017.51.2.139","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
OPERATORS ON THE BESOV SPACES OF HOLOMORPHIC FUNCTIONS ON THE UNIT BALL IN $\mathbb{C}^n$
In the present paper we consider the Toeplitz-$T_{\bar{h}}^{ \alpha}$ and differentiation-$D^\delta $ operators on the Besov spaces $B_p(\beta)$ for all $0< p<\infty.$ We show that $T_{\bar{h}}^{ \alpha}: B_p(\beta)\rightarrow B_p(\beta)$ for $\bar h\in H^\infty(B^n)$ and $D^\delta :B_p(\beta)\rightarrow B_p(\widetilde\beta)$, where $\widetilde\beta=\beta +p\delta .$