Translator Disclaimer
April 2005 Polya's inequalities, global uniform integrability and the size of plurisubharmonic lemniscates
Slimane Benelkourchi, Bensalem Jennane, Ahmed Zeriahi
Author Affiliations +
Ark. Mat. 43(1): 85-112 (April 2005). DOI: 10.1007/BF02383612

Abstract

First we prove a new inequality comparing uniformly the relative volume of a Borel subset with respect to any given complex euclidean ball BCn with its relative logarithmic capacity in Cn with respect to the same ball B. An analogous comparison inequality for Borel subsets of euclidean balls of any generic real subspace of Cn is also proved.

Then we give several interesting applications of these inequalities. First we obtain sharp uniform estimates on the relative size of plurisubharmonic lemniscates associated to the Lelong class of plurisubharmonic functions of logarithmic singularities at infinity on Cn as well as the Cegrell class of plurisubharmonic functions of bounded Monge-Ampère mass on a hyperconvex domain Ω⊂(Cn.

Then we also deduce new results on the global behaviour of both the Lelong class and the Cegrell class of plurisubharmonic functions.

Funding Statement

This work was partially supported by the programmes PARS MI 07 and AI.MA 180.

Citation

Download Citation

Slimane Benelkourchi. Bensalem Jennane. Ahmed Zeriahi. "Polya's inequalities, global uniform integrability and the size of plurisubharmonic lemniscates." Ark. Mat. 43 (1) 85 - 112, April 2005. https://doi.org/10.1007/BF02383612

Information

Received: 18 August 2003; Published: April 2005
First available in Project Euclid: 31 January 2017

zbMATH: 1092.31005
MathSciNet: MR2134700
Digital Object Identifier: 10.1007/BF02383612

Rights: 2005 © Institut Mittag-Leffler

JOURNAL ARTICLE
28 PAGES


SHARE
Vol.43 • No. 1 • April 2005
Back to Top