Sharp norm estimates for the Bergman operator from weighted mixed-norm spaces to weighted Hardy spaces

TL;DR

This paper provides precise bounds for the Bergman operator's norm when mapping from weighted mixed-norm spaces to weighted Hardy spaces within the unit ball, enhancing understanding of operator behavior in complex analysis.

Contribution

It offers the first sharp norm estimates for the Bergman operator between these specific weighted function spaces, filling a gap in the existing literature.

Findings

Established exact norm bounds for the Bergman operator.

Demonstrated the optimality of these bounds.

Extended the analysis to various weighted spaces.

Abstract

In this paper we give sharp norm estimates for the Bergman operator acting from weighted mixed-norm spaces to weighted Hardy spaces in the ball, endowed with natural norms.