The Distribution of Values of Analytic Functions on Convex Bodies

2001/04/27 by A. Brudnyi, Brudnyi, A.
Mathematics · #31B05 #46E15 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #math.CV #math.FA #msc:31B05 #msc:46E15

paper · pdf · doi:10.48550/arxiv.math/0104271

arxiv created 2001/04/27 · arxiv updated 2009/11/30

Abstract

Proceeding the study of local properties of analytic functions started in [Br] we prove new dimensionless inequalities for such functions in terms of their Chebyshev degree. As a consequence, we obtain the reverse Holder inequalities for analytic functions with absolute (i.e., independent of dimension) constants. For polynomials such inequalities were recently proved by Bobkov who sharpened and generalized the previous Bourgain result and by Sodin and Volberg.

Related

• On Local Behavior of Analytic Functions
• The geometric Kannan-Lovasz-Simonovits lemma, dimension-free estimates for volumes of sublevel sets of polynomials, and distribution of zeroes of random analytic functions
• Quantitative tame properties of differentiable functions with controlled derivatives
• Local dimension-free estimates for volumes of sublevel sets of analytic functions
• Doubling condition at the origin for non-negative positive definite\n functions