Weighted composition operators and differences of composition operators between weighted Bergman spaces

Abstract

In this paper, we study weighted composition operators and differences of composition operators. We use the Carleson measure to estimate the operator norm and the essential norm of those operators which act between two Bergman spaces with Békollé weights.

Keywords:

• Békollé weights
• Carleson measures
• differences
• weighted composition operators

AMS SUBJECT CLASSIFICATIONS:

• Primary: 47B33
• 42B35
• Secondary: 32A36
• 47B38

Acknowledgments

This research was performed during the author visit to Washington University in St. Louis. He thanks to Prof. Wick for discussions and Department of Mathematics of Washington University in St. Louis for its hospitality and support. The author thanks the anonymous reviewer(s) for the careful examination of the manuscript and the suggestions.

Disclosure statement

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

Additional information

Funding

Tong was supported in part by the China Scholarship Fund, National Natural Science Foundation of China [grant number 11301132], the Natural Science Foundation of Hebei Province [grant number A2020202005], the Natural Science Foundation of Tianjin City [grant number 20JCYBJC00750] and Overseas Returnees Program of Hebei Province [grant number C201809].