Sobolev spaces on Lie groups: Embedding theorems and algebra properties

被引：20

作者：

Bruno, Tommaso ^{[1
]}

Peloso, Marco M. ^{[2
]}

Tabacco, Anita ^{[1
]}

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：

JOURNAL OF FUNCTIONAL ANALYSIS | 2019年 / 276卷 / 10期

关键词：

Sobolev embeddings; Sobolev algebras; Lie groups; Riesz transforms; MULTIPLIERS;

D O I：

10.1016/j.jfa.2018.11.014

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G be a noncompact connected Lie group, denote with rho a right Haar measure and choose a family of linearly independent left-invariant vector fields X on G satisfying Hormander's condition. Let chi be a positive character of G and consider the measure mu(chi) whose density with respect to rho is chi. In this paper, we introduce Sobolev spaces L-alpha(p)(mu(chi)) adapted to X and mu(chi) (1 < p < infinity, alpha >= 0) and study embedding theorems and algebra properties of these spaces. As an application, we prove local well-posedness and regularity results of solutions of some nonlinear heat and Schrodinger equations on the group. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：3014 / 3050

页数：37

共 34 条

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