2022/09/14 by Chen, Shaolin, Hamada, Hidetaka
#31B05 #31C10 #32U05 #42B30 #46E15 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Primary 42A50
paper · doi:10.48550/arxiv.2209.06625
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 (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 (Acta Math. \bf 178 (1997)~ 143--167) and (Adv. Math. \bf 187 (2004)~ 146--172).