Difference of weighted composition operators

We obtain complete characterizations in terms of Carleson measures for bounded/compact differences of weighted composition operators acting on the standard weighted Bergman spaces over the unit disk. Unlike the known results, we allow the weight functions to be non-holomorphic and unbounded. As a co...

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Bibliographic Details
Published in:Journal of functional analysis 2020-03, Vol.278 (5), p.108401, Article 108401
Main Authors: Choe, Boo Rim, Choi, Koeun, Koo, Hyungwoon, Yang, Jongho
Format: Article
Language:English
Subjects:
Bergman space
Difference
Hardy space
Weighted composition operator
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Summary:We obtain complete characterizations in terms of Carleson measures for bounded/compact differences of weighted composition operators acting on the standard weighted Bergman spaces over the unit disk. Unlike the known results, we allow the weight functions to be non-holomorphic and unbounded. As a consequence we obtain a compactness characterization for differences of unweighted composition operators acting on the Hardy spaces in terms of Carleson measures and, as a nontrivial application of this, we show that compact differences of composition operators with univalent symbols on the Hardy spaces are exactly the same as those on the weighted Bergman spaces. As another application, we show that an earlier characterization due to Acharyya and Wu for compact differences of weighted composition operators with bounded holomorphic weights does not extend to the case of non-holomorphic weights. We also include some explicit examples related to our results.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2019.108401