The Sobolev embedding constant on Lie groups

In this paper we estimate the Sobolev embedding constant on general noncompact Lie groups, for sub-Riemannian inhomogeneous Sobolev spaces endowed with a left invariant measure. The bound that we obtain, up to a constant depending only on the group and its sub-Riemannian structure, reduces to the be...

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Bibliographic Details
Published inNonlinear analysis Vol. 216; p. 112707
Main Authors Bruno, Tommaso, Peloso, Marco M., Vallarino, Maria
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.03.2022
Subjects
Best constant
Lie groups
Moser–Trudinger inequality
Sobolev embeddings
46E35
Moser–Trudinger inequality
26D10
Lie groups
Best constant
Sobolev embeddings
43A80
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Summary:In this paper we estimate the Sobolev embedding constant on general noncompact Lie groups, for sub-Riemannian inhomogeneous Sobolev spaces endowed with a left invariant measure. The bound that we obtain, up to a constant depending only on the group and its sub-Riemannian structure, reduces to the best known bound for the classical inhomogeneous Sobolev embedding constant on Rd. As an application, we prove local and global Moser–Trudinger inequalities.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2021.112707