On the Existence of Extremals for Moser-Type Inequalities in Gauss Space
On the Existence of Extremals for Moser-Type Inequalities in Gauss Space
The existence of an extremal in an exponential Sobolev type inequality, with optimal constant, in Gauss space is established. A key step in the proof is an augmented version of the relevant inequality, which, by contrast, fails for a parallel classical inequality by Moser in the Euclidean space.