Weighted composition operators on extended analytic Lipschitz algebras

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 ۰ < \alpha \leq ۱. 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.

کلیدواژه ها:

Extended analytic Lipschitz algebra‎ ، ‎Analytic uniform algebra‎ ، ‎Banach function algebra‎ ، ‎Compact operator‎ ، ‎Composition operator‎ ، ‎Weighted composition operator