Toeplitz operators and weighted composition operators on variable exponent Bergman spaces

TL;DR

This paper extends the characterization of boundedness and compactness of weighted composition and Toeplitz operators from standard to variable exponent Bergman spaces over the unit ball, providing new proofs and generalizations.

Contribution

It generalizes previous results to variable exponent Bergman spaces and offers new, simplified proofs for these characterizations.

Findings

Characterization of bounded and compact weighted composition operators on variable exponent Bergman spaces.

Characterization of boundedness and compactness of Toeplitz operators on these spaces.

Extension of results from the unit disk and ball to variable exponent settings.

Abstract

In a recent paper [JFA, 278 (2020), 108401], Choe et al. obtained characterizations for bounded and compact differences of two weighted composition operators acting on standard weighted Bergman spaces over the unit disk in terms of Carleson measures. Then they extended the results to the ball setting. In this paper, we further generalize those results to variable exponent Bergman spaces over the unit ball. Our proofs, when restricted to the case of constant variable, are new and simpler. Moreover, boundedness and compactness of Toeplitz operators on variable exponent Bergman spaces are also characterized.