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.
Moser inequalities in Gauss space / Cianchi A.; Musil V.; Pick L.. - In: MATHEMATISCHE ANNALEN. - ISSN 0025-5831. - STAMPA. - 377:(2020), pp. 1265-1312. [10.1007/s00208-020-01956-z]
Moser inequalities in Gauss space
Cianchi A.;Musil V.;
2020
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.
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