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On reverse hypercontractive inequalities

Presented by: 
E Mossel Weizmann Institute of Science
Date: 
Friday 1st April 2011 - 10:00 to 11:00
Venue: 
INI Seminar Room 1
Abstract: 
A hyper-contractive inequality for an operator T states that |Tf|_q \leq |f|_p where q > p > 1 for all functions f. Hyper contractive inequalities play a crucial role in analysis in general and in discrete Fourier analysis in particular.

A reverse hyper-contractive inequality for the operator T states that |Tf|_q \geq |f|_p for q The first reverse hyper-contractive inequalities were proved by Borell more than 2 decades ago. While these inequalities may look obscure, they have been used for the solution of a number of problems in the last decade. I will survey applications of the inequalities and discuss new results relating reverse hyper-contractive inequalities to hyper-contractive, Log-Sobolev and Poincare inequalities as well as some new applications.

This is a joint work with K Oleszkiewicz (Warsaw) and A Sen (Cambridge).
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons