A Sharp inequality for holomorphic functions on the polydisc

2011/05/22 by Marijan Markovic, Markovic, Marijan
Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #math.CV

paper · pdf · doi:10.48550/arxiv.1105.4374

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

arxiv created 2011/09/15 · arxiv updated 2014/03/04

Abstract

In this paper we prove an isoperimetric inequality for holomorphic functions in the unit polydisc \mathbf Uⁿ. 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⊆ A^2p. Also, we extend some results due to Burbea.

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