A Sharp inequality for holomorphic functions on the polydisc

TL;DR

This paper establishes a new isoperimetric inequality for holomorphic functions on the polydisc, leading to generalized space inclusion relations and extending previous results in complex analysis.

Contribution

It introduces a novel inequality for holomorphic functions on the polydisc and generalizes classical space inclusion relations, extending prior work by Burbea.

Findings

Proved an isoperimetric inequality for holomorphic functions on the polydisc.

Derived a generalized inclusion relation between weighted Bergman and Hardy spaces.

Extended existing results in complex analysis related to holomorphic function spaces.

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.