Balayage for the Bergman space

Abstract

We introduce the Bergman space version of the balayage on the unit disk, which we call B-balayage. We show that the B-balayage of a Bergman-Carleson measure satisfies a Lipschitz condition in the Bergman metric. Consequently, the B-balayage of a Bergman-Carleson measure belongs to BMO in the Bergman metric. This extends a classical result about the balayage to the case of Bergman spaces.

Keywords:

• balayage
• Bergman space
• Bergman metric
• BMO

AMS Subject Classifications:

• 30H20
• 32A36
• 30H30

Acknowledgments

All authors are supported by the National Natural Science Foundation of China. The second author is supported by the Innovation Program of Shanghai Municipal Education Commission (no. 13YZ090).