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

Andrea Cianchi; Vít Musil; Luboš Pick

doi:10.1093/imrn/rnaa165

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

Functional Analysis 2023-03-20 v2

Authors: Andrea Cianchi , Vít Musil , Luboš Pick

View on arXiv ↗ PDF ↗ DOI ↗

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

Moser inequality Gauss space extremal function exponential Sobolev inequality optimal constant

Cite

@article{arxiv.2001.02605,
  title  = {On the existence of extremals for Moser type inequalities in Gauss space},
  author = {Andrea Cianchi and Vít Musil and Luboš Pick},
  journal= {arXiv preprint arXiv:2001.02605},
  year   = {2023}
}