Composition operators on Bloch and Hardy type spaces

The main purpose of this paper is to discuss Hardy type spaces, Bloch type spaces and the composition operators of complex-valued harmonic functions. We first establish a sharp estimate of the Lipschitz continuity of complex-valued harmonic functions in Bloch type spaces with respect to the pseudo-h...

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Bibliographic Details
Published in:Mathematische Zeitschrift 2022-08, Vol.301 (4), p.3939-3957
Main Authors: Chen, Shaolin, Hamada, Hidetaka, Zhu, Jian-Feng
Format: Article
Language:English
Subjects:
Composition
Continuity (mathematics)
Harmonic functions
Mathematics
Mathematics and Statistics
Operators (mathematics)
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Summary:The main purpose of this paper is to discuss Hardy type spaces, Bloch type spaces and the composition operators of complex-valued harmonic functions. We first establish a sharp estimate of the Lipschitz continuity of complex-valued harmonic functions in Bloch type spaces with respect to the pseudo-hyperbolic metric, which gives an answer to an open problem. Then some classes of composition operators on Bloch and Hardy type spaces will be investigated. The obtained results improve and extend some corresponding known results.
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-022-03046-z