  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).
