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A sharp inequality for holomorphic functions on the polydisc


Author: Marijan Marković
Journal: Proc. Amer. Math. Soc. 141 (2013), 1693-1704
MSC (2010): Primary 30H10, 32A36, 30A10
Published electronically: November 16, 2012
MathSciNet review: 3020856
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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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Additional Information

Marijan Marković
Affiliation: Faculty of Natural Sciences and Mathematics, University of Montenegro, Cetinjski put b.b., 81000, Podgorica, Montenegro
Email: marijanmmarkovic@gmail.com

DOI: https://doi.org/10.1090/S0002-9939-2012-11446-7
Keywords: Weighted Bergman spaces, Hardy spaces, isoperimetric inequality, polydisc
Received by editor(s): May 27, 2011
Received by editor(s) in revised form: August 9, 2011, and September 9, 2011
Published electronically: November 16, 2012
Communicated by: Franc Forstneric
Article copyright: © Copyright 2012 American Mathematical Society