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arXiv · 2006.07056

The Sobolev embedding constant on Lie groups

Tommaso Bruno·Marco M. Peloso·Maria Vallarino
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Abstract

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 $\mathbb{R}^d$. As an application, we prove local and global Moser--Trudinger inequalities.

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Tommaso Bruno, Marco M. Peloso, Maria Vallarino. 2020-06-12. The Sobolev embedding constant on Lie groups. https://arxiv.org/abs/2006.07056

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