On the Bergman projections acting on $L^\infty$ in the unit ball $\mathbb B_n$

TL;DR

This paper characterizes the radial weights for which the Bergman projection from $L^ fty$ to the Bloch space is bounded in the unit ball of complex n-space, providing insights into weighted Bergman spaces.

Contribution

It offers a characterization of radial weights ensuring boundedness of the Bergman projection from $L^ fty$ to the Bloch space in higher-dimensional unit balls.

Findings

Identifies specific conditions on radial weights for boundedness.

Establishes a link between weighted Bergman spaces and Bloch space.

Provides a criterion for the boundedness of the Bergman projection.

Abstract

Given a weight function, we define the Bergman type projection with values in the corresponding weighted Bergman space on the unit ball $\mathbb B_n$ of $\mathbb C^n, n>1$. We characterize the radial weights such that this projection is bounded from $L^\infty$ to the Bloch space $\mathcal B$.