International Journal of Nonlinear Analysis and Applications

Weighted composition operators on extended analytic Lipschitz algebras

Document Type : Research Paper

Authors

Department of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, Iran

Abstract

 In this paper, we study weighted composition operators on extended analytic Lipschitz algebras ${\rm Lip}_{A}(X,K,\alpha)$ where $X$ is a compact plane set, $K$ is a closed subset of $X$ with nonempty interior and $0 < \alpha \leq 1$. We first give necessary conditions and sufficient conditions on a function $u \in \mathbb{C} ^{X}$ and self-map $\varphi$ of $X$ for which $T=uc_{\varphi}$ to be a weighted composition operator on ${\rm Lip}_{A}(X,K,\alpha)$. We next give the necessary conditions for these operators to be compact and provide some sufficient conditions for the compactness of such operators.

Keywords

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International Journal of Nonlinear Analysis and Applications
Volume 16, Issue 8
August 2025
Pages 121-134
  • Receive Date: 20 December 2023
  • Accept Date: 02 February 2024