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

被引：1

作者：

Hong, Qing ^{[1
]}

Hu, Guorong ^{[1
]}

机构：

[1] Jiangxi Normal Univ, Sch Math & Stat, Nanchang 330022, Jiangxi, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2021年 / 495卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Lie groups of polynomial growth; Functional calculus; Besov space; Triebel-Lizorkin space; Littlewood-Paley decomposition; Smooth atom; DECOMPOSITION; DISTRIBUTIONS;

D O I：

10.1016/j.jmaa.2020.124769

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页数：20

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