Besov and Triebel--Lizorkin spaces on Lie groups

2019/03/14 by Bruno, Tommaso, Peloso, Marco M., Vallarino, Maria · 1 citation
#22E30 #43A15 #46E35 #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1903.05855

Abstract

In this paper we develop a theory of Besov and Triebel--Lizorkin spaces on general noncompact Lie groups endowed with a sub-Riemannian structure. Such spaces are defined by means of hypoelliptic sub-Laplacians with drift, and endowed with a measure whose density with respect to a right Haar measure is a continuous positive character of the group. We prove several equivalent characterizations of their norms, we establish comparison results also involving Sobolev spaces of recent introduction, and investigate their complex interpolation and algebra properties.

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• Strichartz estimates and its application to the well-posedness of the nonlinear Schrödinger equations on H-type groups

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