Characterizations of Sobolev spaces in Euclidean spaces and Heisenberg groups

被引：7

作者：

Cui Xiao-yue ^{[1
]}

Lam Nguyen ^{[1
]}

Lu Guo-zhen ^{[1
]}

机构：

[1] Wayne State Univ, Dept Math, Detroit, MI 48202 USA

来源：

APPLIED MATHEMATICS-A JOURNAL OF CHINESE UNIVERSITIES SERIES B | 2013年 / 28卷 / 04期

关键词：

characterization of Sobelev spaces; Folland-Stein space; Poincare inequalities; Heisenberg group; second order Sobolev space; INTERPOLATION INEQUALITIES; EMBEDDING-THEOREMS; STRATIFIED GROUPS; REPRESENTATION; DEFINITIONS; POLYNOMIALS; CONNECTIONS; FORMULAS;

D O I：

10.1007/s11766-013-3226-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Recently, many new features of Sobolev spaces W (k,p) (a"e (N) ) were studied in [4-6, 32]. This paper is devoted to giving a brief review of some known characterizations of Sobolev spaces in Euclidean spaces and describing our recent study of new characterizations of Sobolev spaces on both Heisenberg groups and Euclidean spaces obtained in [12] and [13] and outlining their proofs. Our results extend those characterizations of first order Sobolev spaces in [32] to the Heisenberg group setting. Moreover, our theorems also provide different characterizations for the second order Sobolev spaces in Euclidean spaces from those in [4, 5].

引用

页码：531 / 547

页数：17

共 36 条

[1]

[Anonymous], 1971, Lecture Notes in Mathematics

[2]

[Anonymous], 1982, Mathematical Notes, DOI DOI 10.1515/9780691222455

[3] APPROXIMATIONS OF SOBOLEV NORMS IN CARNOT GROUPS [J].