Title: Moser meets Gauss
Speaker: Lubos Pick (Charles University)
Abstract: In connection with the study of quantum fields and hypercontractivity semigroups, extensions of the classical Sobolev inequality from the Euclidean space to the setting when the underlying measure space is infinite-dimensional have been investigated. The main motivation for this research is that, in certain circumstances, the study of quantum fields can be reduced to operator or semigroup estimates which are in turn equivalent to inequalities of Sobolev type in infinitely many variables. This led L. Gross in 1975 to his discovery of the so-called logarithmic Sobolev inequalities, which are dimension-independent and which involve functions acting on the Euclidean space endowed with the Gaussian measure. We will focus on questions concerning Moser-type estimates for these spaces.
