On the existence of extremals for Moser type inequalities in Gauss space

Abstract

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.

arXiv comment28 pages

References in corpus (1)

• Moser inequalities in Gauss space

Cited by in corpus (1)

• Optimal Sobolev embeddings for the Ornstein-Uhlenbeck operator