Abstract
We study boundedness and compactness of weighted composition operators on spaces of analytic Lipschitz functions \({\text {Lip}}_A(X, \alpha )\) where X is a compact plane set and \(0<\alpha \le 1\). We give necessary conditions for these operators to be compact, we also provide some sufficient conditions for the compactness of such operators. In the case of \(0<\alpha <1\), to obtain the necessary condition we consider the relationship between these spaces and Bloch type spaces \(\mathcal {B}^\alpha \). We then conclude some results about boundedness and compactness of weighted composition operators on \(\mathcal {B}^\alpha \). Finally, we determine the spectra of compact (Riesz) weighted composition operators acting on analytic Lipschitz spaces or on Bloch type spaces. Also as a consequence, we characterize power compact composition operators on these spaces.
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The authors would like to thank the anonymous referee for several helpful comments to improve the quality of the paper.
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Amiri, S., Golbaharan, A. & Mahyar, H. Weighted Composition Operators on Analytic Lipschitz Spaces. Results Math 73, 46 (2018). https://doi.org/10.1007/s00025-018-0809-6
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DOI: https://doi.org/10.1007/s00025-018-0809-6