A solution of a problem of Enflo - Alexander Volberg скачать в хорошем качестве

A solution of a problem of Enflo - Alexander Volberg

Stony Brook Mathematics Colloquium Video Alexander Volberg, Michigan State University February 11, 2021 Alexander Volberg, Michigan State University A solution of a problem of Enflo How to formulate local notions of Banach space metrically (Ribe program) is important for several reasons: (1) it makes it possible to extend these notions to more general metric spaces; (2) it makes it possible to study embedding in Banach spaces of general metric spaces. Bourgain initiated a program to find explicit metric descriptions of local properties of Banach spaces. In the case of type, the natural conjecture was that Enflo's notion (which predates the Ribe program) is the right one in this context, and this is what we proved with Paata Ivanisvili and Ramon Van Handel. The proof is based on a novel dimension-free analogue of Pisier's inequality on the Hamming cube, which, in its turn, is based on a certain formula that we used before in improving the constants in scalar Poincare inequality on Hamming cube. In the second part of the presentation, if time permits, I will talk about singular integrals on Hamming cube and about two approaches: Lust-Piquard's approach via quantum random variable and another approach using Bellman function technique. Slides: https://www.math.stonybrook.edu/Video...