A note on Stevi\'c-Sharma type operators between Bergman spaces with doubling weights

TL;DR

This paper characterizes the boundedness and compactness of Stević-Sharma type operators with varying weights and composition symbols between Bergman spaces with doubling weights, extending previous estimates.

Contribution

It provides a complete characterization of these operators' boundedness and compactness between weighted Bergman spaces with doubling weights.

Findings

Identifies conditions for boundedness of the operators.

Establishes criteria for compactness of the operators.

Extends previous results to more general weights and symbols.

Abstract

Using some estimates in [J. Funct. Anal. {\bf 278}(2020), Article No. 108401], we completely characterized the boundedness and compactness of the Stevi\'c-Sharma type operators with different weights and different composition symbols between Bergman spaces induced by two-sides doubling weights.