Equivalent quasi-norms in Besov and Triebel-Lizorkin spaces on Lie groups of polynomial growth

Let G be a Lie group of polynomial growth and X = {X-1 , ... , X-n} be a family of left-invariant vector fields on G satisfying the Hormander condition. In this paper, by utilizing smooth atomic decomposition, we obtain equivalent quasi-norm characterizations for Besov and Triebel-Lizorkin spaces F-p,q(s)(G) on G associated with the vector fields X, for full range of indices. This extends related classical results on the Euclidean spaces. (C) 2020 Elsevier Inc. All rights reserved.

Automated summary

By utilizing smooth atomic decomposition, equivalent quasi-norm characterizations for Besov and Triebel-Lizorkin spaces on a Lie group of polynomial growth associated with left-invariant vector fields are obtained in this paper, extending related classical results on Euclidean spaces.