Global estimates in Sobolev spaces for homogeneous Hormander sums of squares

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:498

Article

Biagi, Stefano¹  Bonfiglioli, Andrea²  Bramanti, Marco¹ 

[1] Politecn Milan, Dipartimento Matemat, Via Bonardi 9, I-20133 Milan, Italy

[2] Univ Bologna, Alma Mater Studiorum, Dipartimento Matemat, Piazza Porta San Donato 5, I-40126 Bologna, Italy

关键词: A priori estimates;    Sobolev spaces;    Regularity of solutions;    Interpolation inequalities;   

DOI  :  10.1016/j.jmaa.2021.124935

来源: Elsevier

【 摘 要 】

Let L = Sigma(m)(j=1) X-j(2) be a Hormander sum of squares of vector fields in space R-n, where any X-j is homogeneous of degree 1 with respect to a family of non-isotropic dilations in space. In this paper we prove global estimates and regularity properties for L in the X-Sobolev spaces W-X(k,p) (R-n), where X = {X-1, ... , X-m}. In our approach, we combine local results for general Hormander sums of squares, the homogeneity property of the X-j's, plus a global lifting technique for homogeneous vector fields. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free