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The Distribution of Values of Analytic Functions on Convex Bodies

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arxiv math/0104271 v1 pith:B2CR7I4L submitted 2001-04-27 math.CV math.FA

A.Brudnyi This is my paper · ORCID
classification math.CVmath.FA
keywords functionsanalyticinequalitiesabsolutebobkovbodiesbourgainchebyshev
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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.

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