Composition operators over weighted Bergman spaces of Dirichlet series

ABSTRACT

In the paper ‘Composition operators on weighted Bergman spaces of Dirichlet series. J Math Anal Appl. 2015;426:340–363’, Bailleul completely characterized the boundedness of composition operators on weighted Bergman spaces of Dirichlet series for the case of symbols with $c_0\ge 1$. But the sufficient conditions for the other case $c_0=0$ were unsolved. In this paper, we follow this line and study the boundedness of composition operators on weighted Bergman spaces of Dirichlet series for the case $c_0=0$. Moreover, we also obtain the compact characterizations of composition operators with $c_0\ge 1$.

KEYWORDS:

• Composition operator
• weighted Bergman space
• Dirichlet series

AMS SUBJECT CLASSIFICATIONS:

• Primary: 47B33
• Secondary: 32A36

Acknowledgements

The authors are sincerely grateful to the anonymous referee for his/her valuable suggestions which helped to improve the presentation of the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This project was partially supported by NSFC [11771340].