Journal
MATHEMATISCHE ZEITSCHRIFT
Volume 301, Issue 4, Pages 3939-3957Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s00209-022-03046-z
Keywords
Bloch type space; Complex-valued harmonic function; Composition operator; Hardy type space
Categories
Funding
- National Science Foundation of China [12071116, 11501220, 11971182, 2021J01304, 2019J01066]
- Hunan Natural Science outstanding youth fund project
- Key Projects of Hunan Provincial Department of Education [21A0429]
- Double First-Class University Project of Hunan Province [[2018]469]
- Science and Technology Plan Project of Hunan Province [2016TP1020]
- Discipline Special Research Projects of Hengyang Normal University [XKZX21002]
- JSPS KAKENHI [JP19K03553]
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The main purpose of this paper is to discuss Hardy type spaces, Bloch type spaces, and composition operators of complex-valued harmonic functions. It first establishes a sharp estimate for the Lipschitz continuity of complex-valued harmonic functions in Bloch type spaces, providing an answer to an open problem. Several classes of composition operators on Bloch and Hardy type spaces are then investigated, improving and extending previous known results.
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.
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