Complex symmetric Weighted Composition--Differentiation Operators of order $n$ on the Weighted Bergman Spaces

TL;DR

This paper investigates the complex symmetric properties of weighted composition--differentiation operators of order n on weighted Bergman spaces, providing theoretical insights and specific examples.

Contribution

It introduces the study of complex symmetry for these operators on weighted Bergman spaces and offers explicit examples illustrating the concepts.

Findings

Identification of complex symmetric structures of the operators

Examples demonstrating the theoretical results

Insights into the behavior of weighted composition--differentiation operators

Abstract

We study the complex symmetric structure of weighted composition--differentiation operators of order $n $ on the weighted Bergman spaces $A_{\alpha}^2$ with respect to some conjugations. Then we provide some examples of these operators.