Toeplitz operators and Carleson measure between weighted Bergman spaces induced by regular weights

TL;DR

This paper characterizes when Toeplitz operators are bounded or compact between weighted Bergman spaces with regular weights, providing a new measure criterion based on Khinchin's and Kahane's inequalities.

Contribution

It offers a universal description of Toeplitz operator boundedness and compactness between weighted Bergman spaces with regular weights, introducing a new Carleson measure characterization.

Findings

New characterization of Carleson measures for regular-weight Bergman spaces

Universal criteria for Toeplitz operator boundedness and compactness

Application of Khinchin's and Kahane's inequalities in analysis

Abstract

In this paper, we give a universal description of the boundedness and compactness of Toeplitz operator $\mathcal{T}_\mu^\omega$ between Bergman spaces $A_\eta^p$ and $A_\upsilon^q$ when $\mu$ is a positive Borel measure, $1<p,q<\infty$ and $\omega,\eta,\upsilon$ are regular weights. By using Khinchin's inequality and Kahane's inequality, we get a new characterization of the Carleson measure for Bergman spaces induced by regular weights.