Toeplitz operators on Bergman spaces induced by doubling weights on the unit ball of $\mathbb{C}^n$

TL;DR

This paper investigates the properties of Toeplitz operators on weighted Bergman spaces in complex n-dimensional unit balls, focusing on boundedness, compactness, and Schatten class characterizations.

Contribution

It provides new characterizations of Toeplitz operators with doubling weights, including criteria for boundedness, compactness, and Schatten class membership.

Findings

Characterization of bounded and compact Toeplitz operators on weighted Bergman spaces.

Criteria for Schatten class Toeplitz and Volterra operators on $A_ ext{omega}^2$.

Extension of operator theory in complex analysis with doubling weights.

Abstract

The boundedness and compactness of Toeplitz operator from $A_\omega^p$ to $A_\omega^q$ with doubling weights $\omega$ are studied in this paper. The characterizations of Schatten class Toeplitz operators and Volterra operators on $A_\omega^2$ are also investigated.