Equivalent norms and Hardy-Littlewood type Theorems, and their applications
Abstract
The main purpose of this paper is to develop some methods to investigate equivalent norms and Hardy-Littlewood type Theorems on Lipschitz type spaces of analytic functions and complex-valued harmonic functions. Initially, some characterizations of equivalent norms on Lipschitz type spaces of analytic functions and complex-valued harmonic functions will be given. In particular, we give an answer to an open problem posed by Dyakonov in (Math. Z.249(2005), 597--611). Furthermore, some Hardy-Littlewood type Theorems of complex-valued harmonic functions are established. The obtained results improve and extend the main results in (Acta Math.178(1997),143--167). Additionally, we apply the equivalent norms and Hardy-Littlewood type Theorems to study composition operators between Lipschitz type spaces.
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Cite
@article{arxiv.2304.01465,
title = {Equivalent norms and Hardy-Littlewood type Theorems, and their applications},
author = {Shaolin Chen and Hidetaka Hamada},
journal= {arXiv preprint arXiv:2304.01465},
year = {2023}
}
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36 pages