Moser inequalities in Gauss space

Abstract

The sharp constants in a family of exponential Sobolev type inequalities in Gauss space are exhibited. They constitute the Gaussian analogues of the Moser inequality in the borderline case of the Sobolev embedding in the Euclidean space. Interestingly, the Gaussian results have features in common with the Euclidean ones, but also reveal marked diversities.

arXiv commentAccepted in Mathematische Annalen

Cited by in corpus (3)

• Optimal Sobolev embeddings for the Ornstein-Uhlenbeck operator
• On the existence of extremals for Moser type inequalities in Gauss space
• Sharp exponential inequalities for the Ornstein-Uhlenbeck operator