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arXiv · 2304.01465

Equivalent norms and Hardy-Littlewood type Theorems, and their applications

Shaolin Chen·Hidetaka Hamada
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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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Shaolin Chen, Hidetaka Hamada. 2023-04-04. Equivalent norms and Hardy-Littlewood type Theorems, and their applications. https://arxiv.org/abs/2304.01465

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