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arXiv · 2209.06625

On Riesz type inequalities, Hardy-Littlewood type theorems and smooth moduli

Shaolin Chen·Hidetaka Hamada
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Abstract

The purpose of this paper is to develop some methods to study Riesz type inequalities, Hardy-Littlewood type theorems and smooth moduli of holomorphic, pluriharmonic and harmonic functions in high-dimensional cases. Initially, we prove some sharp Riesz type inequalities of pluriharmonic functions on bounded symmetric domains. The obtained results extend the main results in (\textit{Trans. Amer. Math. Soc.} {\bf 372} (2019)~ 4031--4051). Furthermore, some Hardy-Littlewood type theorems of holomorphic and pluriharmonic functions on John domains are established. Additionally, we also discuss the Hardy-Littlewood type theorems and smooth moduli of holomorphic, pluriharmonic and harmonic functions. Consequently, we improve and generalize the corresponding results in (\textit{Acta Math.} {\bf 178} (1997)~ 143--167) and (\textit{Adv. Math.} {\bf 187} (2004)~ 146--172).

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Shaolin Chen, Hidetaka Hamada. 2022-09-14. On Riesz type inequalities, Hardy-Littlewood type theorems and smooth moduli. https://arxiv.org/abs/2209.06625

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