GENERALIZED CESÀRO OPERATORS ON DIRICHLET-TYPE SPACES

doi:10.1007/s10473-022-0111-2

数学物理学报(英文版) ›› 2022, Vol. 42 ›› Issue (1): 212-220.doi: 10.1007/s10473-022-0111-2

GENERALIZED CESÀRO OPERATORS ON DIRICHLET-TYPE SPACES

金建军¹, 唐树安²

1. School of Mathematics Sciences, Hefei University of Technology, Xuancheng Campus, Xuancheng, 242000, China;
2. School of Mathematics Sciences, Guizhou Normal University, Guiyang, 550001, China

收稿日期:2020-07-25 修回日期:2021-06-02 出版日期:2022-02-25 发布日期:2022-02-24
通讯作者: Jianjun JIN,E-mail:jin@hfut.edu.cn E-mail:jin@hfut.edu.cn
作者简介:Shuan TANG,E-mail:tsa@gznu.edu.cn
基金资助:
The first author was supported by National Natural Science Foundation of China (11501157). The second author was supported by National Natural Science Foundation of China (12061022) and the foundation of Guizhou Provincial Science and Technology Department ([2017]7337 and[2017]5726).

GENERALIZED CESÀRO OPERATORS ON DIRICHLET-TYPE SPACES

Jianjun JIN¹, Shuan TANG²

1. School of Mathematics Sciences, Hefei University of Technology, Xuancheng Campus, Xuancheng, 242000, China;
2. School of Mathematics Sciences, Guizhou Normal University, Guiyang, 550001, China

Received:2020-07-25 Revised:2021-06-02 Online:2022-02-25 Published:2022-02-24
Contact: Jianjun JIN,E-mail:jin@hfut.edu.cn E-mail:jin@hfut.edu.cn
Supported by:
The first author was supported by National Natural Science Foundation of China (11501157). The second author was supported by National Natural Science Foundation of China (12061022) and the foundation of Guizhou Provincial Science and Technology Department ([2017]7337 and[2017]5726).

摘要/Abstract

摘要： In this note, we introduce and study a new kind of generalized Cesàro operator, $\mathcal{C}_{\mu}$ , induced by a positive Borel measure $\mu$ on $[0, 1)$ between Dirichlet-type spaces. We characterize the measures $\mu$ for which $\mathcal{C}_{\mu}$ is bounded (compact) from one Dirichlet-type space, $\mathcal{D}_{\alpha}$ , into another one, $\mathcal{D}_{\beta}$ .

关键词: generalized Cesàro operator, Dirichlet-type spaces, Carleson measure, boundedness and compactness of operator

Abstract: In this note, we introduce and study a new kind of generalized Cesàro operator, $\mathcal{C}_{\mu}$ , induced by a positive Borel measure $\mu$ on $[0, 1)$ between Dirichlet-type spaces. We characterize the measures $\mu$ for which $\mathcal{C}_{\mu}$ is bounded (compact) from one Dirichlet-type space, $\mathcal{D}_{\alpha}$ , into another one, $\mathcal{D}_{\beta}$ .

Key words: generalized Cesàro operator, Dirichlet-type spaces, Carleson measure, boundedness and compactness of operator

中图分类号:

47B38

金建军, 唐树安. GENERALIZED CESÀRO OPERATORS ON DIRICHLET-TYPE SPACES[J]. 数学物理学报(英文版), 2022, 42(1): 212-220.

Jianjun JIN, Shuan TANG. GENERALIZED CESÀRO OPERATORS ON DIRICHLET-TYPE SPACES[J]. Acta mathematica scientia,Series B, 2022, 42(1): 212-220.

参考文献

[1] Aleman A. A class of integral operators on spaces of analytic functions//Proceedings of the Winter School in Operator Theory and Complex Analysis. Málaga:Univ Málaga Secr Publ, 2007:3-30
[2] Aleman A, Cima J. An integral operator on H^p and Hardy's inequality. J Anal Math, 2001, 85:157-176
[3] Aleman A, Siskakis A. Integration operators on Bergman spaces. Indiana Univ Math J, 1997, 46(2):337- 356
[4] Galanopoulos P. The Cesàro operator on Dirichlet spaces. Acta Sci Math (Szeged), 2001, 67:411-420
[5] Hu Z. Extende Cesàro operators on the Bloch space in the unit ball of

$\mathbb{C}^n$ . Acta Math Sci, 2003, 23B(4):561-566
[6] Miller V, Miller T, The Cesàro operator on the Bergman space

$A^2(\mathbb{D})$ . Arch Math, 2002, 78(5):409-416
[7] Siskakis A. The Cesàro operator is bounded on H¹. Proc Amer Math Soc, 1990, 110(2):461-462
[8] Siskakis A. On the Bergman space norm of the Cesàro operator. Arch Math, 1996, 67(4):312-318
[9] Xiao J. Cesàro-type operators on Hardy, BMOA and Bloch spaces. Arch Math, 1997, 68:398-406
[10] Stempak K. Cesàro averaging operators. Proc Royal Soc Edinburgh Section A:Math, 1994, 124:121-126
[11] Wang Z, Gua D. An Introduction to Special Functions. Beijing:Science Press, 1979
[12] Zhu K. Operator Theory in Function Spaces. New York:Marcel Dekker, 1990

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GENERALIZED CESÀRO OPERATORS ON DIRICHLET-TYPE SPACES

GENERALIZED CESÀRO OPERATORS ON DIRICHLET-TYPE SPACES

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