# Weighted Composition Operators on Analytic Lipschitz Spaces

Weighted Composition Operators on Analytic Lipschitz Spaces We study boundedness and compactness of weighted composition operators on spaces of analytic Lipschitz functions $${\text {Lip}}_A(X, \alpha )$$ Lip A ( X , α ) where X is a compact plane set and $$0<\alpha \le 1$$ 0 < α ≤ 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 $$0<\alpha <1$$ 0 < α < 1 , to obtain the necessary condition we consider the relationship between these spaces and Bloch type spaces $$\mathcal {B}^\alpha$$ B α . We then conclude some results about boundedness and compactness of weighted composition operators on $$\mathcal {B}^\alpha$$ B α . 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Results in Mathematics Springer Journals

# Weighted Composition Operators on Analytic Lipschitz Spaces

, Volume 73 (1) – Feb 23, 2018
15 pages

/lp/springer_journal/weighted-composition-operators-on-analytic-lipschitz-spaces-PfTr0TSXUA
Publisher
Springer International Publishing
Copyright © 2018 by Springer International Publishing AG, part of Springer Nature
Subject
Mathematics; Mathematics, general
ISSN
1422-6383
eISSN
1420-9012
D.O.I.
10.1007/s00025-018-0809-6
Publisher site
See Article on Publisher Site

### Abstract

We study boundedness and compactness of weighted composition operators on spaces of analytic Lipschitz functions $${\text {Lip}}_A(X, \alpha )$$ Lip A ( X , α ) where X is a compact plane set and $$0<\alpha \le 1$$ 0 < α ≤ 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 $$0<\alpha <1$$ 0 < α < 1 , to obtain the necessary condition we consider the relationship between these spaces and Bloch type spaces $$\mathcal {B}^\alpha$$ B α . We then conclude some results about boundedness and compactness of weighted composition operators on $$\mathcal {B}^\alpha$$ B α . 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.

### Journal

Results in MathematicsSpringer Journals

Published: Feb 23, 2018

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