A Sharp inequality for holomorphic functions on the polydisc

Marijan Markovic

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arXiv · 1105.4374

A Sharp inequality for holomorphic functions on the polydisc

Marijan Markovic

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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.

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Marijan Markovic. 2011-05-22. A Sharp inequality for holomorphic functions on the polydisc. https://arxiv.org/abs/1105.4374

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