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.

Keywords

• logarithmic sobolev inequalities
• trudinger inequalities
• sharp form
• unbounded-domains
• boundary
• compactness
• imbeddings
• laplacian