Dyadic Carleson embedding and sparse domination of weighted composition operators on strictly pseudoconvex domains

TL;DR

This paper investigates weighted composition operators on Bergman spaces over strictly pseudoconvex domains, employing sparse domination techniques to establish new weighted estimates and extend previous results in a broader context.

Contribution

It introduces a novel approach using sparse domination for weighted composition operators on complex domains, generalizing earlier work and providing new weighted estimates.

Findings

Established a weighted type estimate for the operators.

Extended previous results to more general strictly pseudoconvex domains.

Applied harmonic analysis techniques to complex analysis operators.

Abstract

In this paper, we study the behavior of the weighted composition operators acting on Bergman spaces defined on strictly pseudoconvex domains via the sparse domination technique from harmonic analysis. As a byproduct, we also prove a weighted type estimate for the weighted composition operators which is adapted to Sawyer-testing conditions. Our results extend the work by the first author, Li, Shi and Wick under a much more general setting.