A Sharp inequality for holomorphic functions on the polydisc

Abstract

In this paper we prove an isoperimetric inequality for holomorphic functions in the unit polydisc $\mathbf U^n$. As a corollary we derive an inclusion relation between weighted Bergman and Hardy spaces of holomorphic functions in the polydisc which generalizes the classical Hardy--Littlewood relation $H^p\subseteq A^{2p}$. Also, we extend some results due to Burbea.