A sharp inequality for holomorphic functions on the polydisc

Marković, Marijan

doi:10.1090/S0002-9939-2012-11446-7

A sharp inequality for holomorphic functions on the polydisc
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Proc. Amer. Math. Soc. 141 (2013), 1693-1704 Request permission

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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