Definitions of Sobolev classes on metric spaces

被引：112

作者：

Franchi, B

Hajlasz, P

Koskela, P

机构：

[1] Univ Bologna, Dipartmento Matemat, I-40127 Bologna, Italy

[2] Warsaw Univ, Inst Math, PL-02097 Warsaw, Poland

[3] Univ Jyvaskyla, Dept Math, FIN-40351 Jyvaskyla, Finland

来源：

ANNALES DE L INSTITUT FOURIER | 1999年 / 49卷 / 06期

关键词：

Sobolev spaces; metric spaces; doubling measures; Carnot-Caratheodory spaces; hormander's rank condition;

D O I：

10.5802/aif.1742

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

There have been recent attempts to develop the theory of Sobolev spaces W-1.p on metric spaces that do not admit any differentiable structure. We prove that certain definitions are equivalent. We also define the spaces in the limiting case p = 1.

引用

页码：1903 / +

页数：23

共 23 条

[1]

Dellacherie C., 1978, N HOLLAND MATH STUDI, V29

[2] THE LOCAL REGULARITY OF SOLUTIONS OF DEGENERATE ELLIPTIC-EQUATIONS [J].

FABES, EB ;

KENIG, CE ;

SERAPIONI, RP .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1982, 7 (01) :77-116

[3] WEIGHTED SOBOLEV-POINCARE INEQUALITIES FOR GRUSHIN TYPE OPERATORS [J].

FRANCHI, B ;

GUTIERREZ, CE ;

WHEEDEN, RL .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1994, 19 (3-4) :523-604

[4]

Franchi B, 1997, B UNIONE MAT ITAL, V11B, P83

[5] Self-improving properties of John-Nirenberg and Poincare inequalities on spaces of homogeneous type [J].

Franchi, B ;

Perez, C ;

Wheeden, RL .

JOURNAL OF FUNCTIONAL ANALYSIS, 1998, 153 (01) :108-146

[6]

Franchi B., 1983, Ann. Sc. Norm. Super. Pisa, Cl. Sci., VIV, P523

[7]

FRANCHI B., 1996, Int. Math. Res. Not. IMRN, V1996, P1

[8]

Garofalo N, 1996, COMMUN PUR APPL MATH, V49, P1081, DOI 10.1002/(SICI)1097-0312(199610)49:10<1081::AID-CPA3>3.0.CO

[9]

2-A

[10] Lipschitz continuity, global smooth approximations and extension theorems for Sobolev functions in Carnot-Caratheodory spaces [J].

Garofalo, N ;

Nhieu, DM .

JOURNAL D ANALYSE MATHEMATIQUE, 1998, 74 (1) :67-97

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