Carleson Measures and Toeplitz operators for weighted Bergman spaces on the unit ball

TL;DR

This paper provides new characterizations of Carleson measures and Toeplitz operators for weighted Bergman spaces on the unit ball, with applications to Cesàro and multiplication operators, extending known results even in the unit disk case.

Contribution

It introduces novel characterizations involving product functions for Carleson measures and operator boundedness in weighted Bergman spaces.

Findings

Characterizations of Carleson measures involving product functions.

Criteria for bounded and compact Toeplitz operators.

Extensions to Cesàro and multiplication operators, even in the unit disk.

Abstract

Some new characterizations on Carleson measures for weighted Bergman spaces on the unit ball involving product of functions are obtained. For these we characterize bounded and compact Toeplitz operators between weighted Bergman spaces. The above results are applied to characterize bounded and compact extended Ces\`aro operators and pointwise multiplication operators. The results are new even in the case of the unit disk.