Title

On concentration, deviation and Dvoretzky's theorem for Besov, Lizorkin-Triebel and other spaces

RIS ID

103655

Publication Details

Ajiev, S. (2010). On concentration, deviation and Dvoretzky's theorem for Besov, Lizorkin-Triebel and other spaces. Complex Variables and Elliptic Equations: an international journal, 55 (8-10), 693-726.

Abstract

We obtain explicit estimates of the constants related to the concentrations of measures and distance, deviation and Dvoretzky's theorem for the finite-dimensional subspaces of a wide class of function and other spaces including, in particular, various anisotropic spaces of Besov, Lizorkin- Triebel and Sobolev types endowed with geometrically friendly norms defined in terms of averaged differences, local polynomial approximations, functional calculus, wavelets and other means. New approaches are shown to be providing better estimates in the abstract setting as well.

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