The anisotropic spaces of functions defined on open subsets of a Euclidean spaces of Besov and Lizorkin-Triebel type endowed with various norms and a wide class of independently generated spaces introduced earlier are considered along with the subspaces of all these spaces and their duals. The norms include those defined in terms of differences, local approximations, functional calculus, as well as wavelet norms.

In a quantitative and uniform manner, we investigate the deviation and the concentration of measure and distance phenomena on subsets of finite-dimensional subspaces of the spaces under consideration following and comparing both classical and new approaches.

As an application, one establishes explicit estimates constituting the Dvoretzky theorem for finite-dimensional subspaces of all the spaces mentioned above by means of a modification of Schechtman's development of V. Milman's approach and its alternative.


Dr. Sergey Ajiev

Research Area

Analysis Seminar




Wed, 06/05/2009 - 12:00pm