Weighted Estimates for Operators Associated to the Bergman-Besov Kernels

TL;DR

This paper characterizes the weights ensuring boundedness of integral operators related to Bergman-Besov kernels on weighted Lebesgue spaces in the unit ball of complex space, using Békollé-Bonami conditions.

Contribution

It provides a new characterization of weights for boundedness of Bergman-Besov related operators via Békollé-Bonami type conditions.

Findings

Established necessary and sufficient conditions for weight boundedness.

Extended Békollé-Bonami theory to Bergman-Besov kernels.

Applicable to operators on weighted Lebesgue spaces in complex analysis.

Abstract

We characterize the weights for which we have the boundedness of standard weighted integral operators induced by the Bergman-Besov kernels acting between two general weighted Lebesgue classes on the unit ball of $\mathbb{C}^N$ in terms of B\'ekoll\'e - Bonami type condition on the weights. To accomplish this we employ the proof strategy originated by B\'ekoll\'e.