Carleson-Type Measures and Kernel Estimates for Potential-Harmonic Weighted Bergman Spaces on the Unit Ball

TL;DR

This paper studies weighted Bergman spaces on the unit ball in complex space, providing characterizations of Carleson measures and estimates for the reproducing kernel functions, advancing understanding of their structure and embeddings.

Contribution

It offers new characterizations of Carleson embeddings and derives pointwise and norm estimates for the reproducing kernels in weighted Bergman spaces.

Findings

Characterization of Carleson measures for weighted Bergman spaces

Pointwise estimates of the reproducing kernel functions

Norm estimates for the reproducing kernels

Abstract

In this paper, weighted Bergman spaces on the unit ball in C^n are investigated. A characterization of the Carleson embeddings is established. Pointwise and norm estimates on the reproducing kernel function of weighted Bergman spaces on the unit ball are proved.