The Sobolev embedding constant on Lie groups

2020/06/12 by Tommaso Bruno, Bruno, Tommaso, Marco M. Peloso +3
Mathematics · #26D10 #43A80 #46E35 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #math.AP #math.CA #math.FA #msc:26D10 #msc:43A80 #msc:46E35

paper · pdf · doi:10.48550/arxiv.2006.07056

19 pages

arxiv created 2021/11/16 · arxiv updated 2021/11/17

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 ℝ^d. As an application, we prove local and global Moser--Trudinger inequalities.

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