A Sharp inequality for holomorphic functions on the polydisc

Details A Sharp inequality for holomorphic functions on the polydisc A Sharp inequality for holomorphic functions on the polydisc

2011-05-22

arxiv.org/abs/1105.4374v3

Mathematics

Complex Variables

13 pages; Proc. Amer. Math. Soc. 2011

Scientific paper

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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