Moser inequalities in Gauss space

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 wi...

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Bibliographic Details
Published in:Mathematische annalen 2020-08, Vol.377 (3-4), p.1265-1312
Main Authors: Cianchi, Andrea, Musil, Vít, Pick, Luboš
Format: Article
Language:English
Subjects:
Euclidean geometry
Euclidean space
Inequalities
Mathematics
Mathematics and Statistics
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Summary: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.
ISSN:0025-5831
1432-1807
DOI:10.1007/s00208-020-01956-z