GENERALIZED COUNTING FUNCTIONS AND COMPOSITION OPERATORS ON WEIGHTED BERGMAN SPACES OF DIRICHLET SERIES

GENERALIZED COUNTING FUNCTIONS AND COMPOSITION OPERATORS ON WEIGHTED BERGMAN SPACES OF DIRICHLET SERIES

GENERALIZED COUNTING FUNCTIONS AND COMPOSITION OPERATORS ON WEIGHTED BERGMAN SPACES OF DIRICHLET SERIES

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doi:10.1007/s10473-025-0201-z

Acta mathematica scientia,Series B ›› 2025, Vol. 45 ›› Issue (2): 291-309.doi: 10.1007/s10473-025-0201-z

Min He¹, Maofa Wang², Jiale Chen^3,*

1. School of Information and Mathematics, Yangtze University, Jingzhou 434023, China;
2. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China;
3. School of Mathematics and Statistics, Shaanxi Normal University, Xi'an 710119, China

Received:2023-11-09 Revised:2024-05-28 Online:2025-03-25 Published:2025-05-08
Contact: *Jiale Chen, E-mail: jialechen@snnu.edu.cn
About author:Min He, E-mail: hm.math@whu.edu.cn;Maofa Wang, E-mail: mfwang.math@whu.edu.cn
Supported by:
This work was partially supported by the National Natural Science Foundation of China (12171373). Chen's work also supported by the Fundamental Research Funds for the Central Universities of China (GK202207018).

Abstract: In this paper, we study composition operators on weighted Bergman spaces of Dirichlet series. We first establish some Littlewood-type inequalities for generalized mean counting functions. Then we give sufficient conditions for a composition operator with zero characteristic to be bounded or compact on weighted Bergman spaces of Dirichlet series. The corresponding sufficient condition for compactness in the case of positive characteristics is also obtained.

Key words: generalized counting function, Dirichlet series, composition operator, weighted Bergman space

CLC Number:

47B33

Min He, Maofa Wang, Jiale Chen. GENERALIZED COUNTING FUNCTIONS AND COMPOSITION OPERATORS ON WEIGHTED BERGMAN SPACES OF DIRICHLET SERIES[J].Acta mathematica scientia,Series B, 2025, 45(2): 291-309.

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