Besov and Triebel-Lizorkin spaces on Lie groups

被引：12

作者：

Bruno, Tommaso ^{[1
]}

Peloso, Marco M. ^{[2
]}

Vallarino, Maria ^{[1
]}

机构：

[1] Politecn Torino, Dipartimento Eccellenza 2018 2022, Dipartimento Sci Matemat Giuseppe Luigi Lagrange, Corso Duca Abruzzi 24, I-10129 Turin, Italy

[2] Univ Milan, Dipartimento Matemat, Via C Saldini 50, I-20133 Milan, Italy

来源：

MATHEMATISCHE ANNALEN | 2020年 / 377卷 / 1-2期

关键词：

HARDY-SOBOLEV SPACES; ALGEBRA PROPERTIES; HEAT KERNEL;

D O I：

10.1007/s00208-019-01927-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we develop a theory of Besov and Triebel-Lizorkin spaces on general noncompact connected 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.

引用

页码：335 / 377

页数：43

共 36 条

[1] The intrinsic hypoelliptic Laplacian and its heat kernel on unimodular Lie groups [J].