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Annals of Mathematics, II. Series Vol. 149, No. 2, pp. 511533 (1999) 

Local inequalities for plurisubharmonic functionsAlexander BrudnyiReview from Zentralblatt MATH:
The main result is the following: there are constants $c=c(a,r)$ and $d=d(n)$ such that the inequality $$\sup_{B(x,t)}f\leq c\log\left(\frac{d B(x,t) }{ \omega }\right)+\sup_{\omega}f$$ holds for every $f\in\cal{F}_r$ and every measurable subset $\omega\subset B(x,t)$. The author gives applications of the main theorem related to Yu. BrudnyiGanzburg type inequalities for polynomials, algebraic functions and entire functions of exponential type. He also gives applications to logBMO properties of real analytic functions, which were known previously only for polynomials. Reviewed by K.G.Malyutin Keywords: plurisubharmonic function; BMOfunction; Euclidean ball; BrudnyiGanzburg type inequality Classification (MSC2000): 31C10 32U05 31B05 46E15 Full text of the article:
Electronic fulltext finalized on: 8 Sep 2001. This page was last modified: 21 Jan 2002.
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