Characterizations of Besov and Triebel-Lizorkin spaces on metric measure spaces

被引：62

作者：

Gogatishvili, Amiran ^{[1
]}

Koskela, Pekka ^{[2
]}

Zhou, Yuan ^{[2
,3
]}

机构：

[1] Acad Sci Czech Republ, Inst Math, CR-11567 Prague 1, Czech Republic

[2] Univ Jyvaskyla, Dept Math & Stat, FI-40014 Jyvaskyla, Finland

[3] Beijing Univ Aeronaut & Astronaut, Dept Math, Beijing 100083, Peoples R China

来源：

FORUM MATHEMATICUM | 2013年 / 25卷 / 04期

基金：

芬兰科学院;

关键词：

Besov space; Triebel-Lizorkin space; Hajlasz-Besov space; Hajlasz-Triebel-Lizorkin space; metric measure space; sharp maximal function; SOBOLEV SPACES; MAXIMAL FUNCTIONS; INEQUALITY; EXTENSION;

D O I：

10.1515/FORM.2011.135

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

On a metric measure space satisfying the doubling property, we establish several optimal characterizations of Besov and Triebel-Lizorkin spaces, including a pointwise characterization. Moreover, we discuss their (non) triviality under a Poincare inequality.

引用

页码：787 / 819

页数：33

共 28 条

[1]

[Anonymous], 2010, Theory of Function Spaces

[2]

Bourdon M, 2003, J REINE ANGEW MATH, V558, P85

[3] ESTIMATES FOR SINGULAR INTEGRAL OPERATORS IN TERMS OF MAXIMAL FUNCTIONS [J].

CALDERON, AP .

STUDIA MATHEMATICA, 1972, 44 (06) :563-582

[4] THE EXTENSION PROBLEM FOR CERTAIN FUNCTION-SPACES INVOLVING FRACTIONAL ORDERS OF DIFFERENTIABILITY [J].

CHRIST, M .

ARKIV FOR MATEMATIK, 1984, 22 (01) :63-81

[5]

DEVORE RA, 1984, MEM AM MATH SOC, V47, P1

[6] A CONDITION FOR A 2-WEIGHT NORM INEQUALITY FOR SINGULAR INTEGRAL-OPERATORS [J].

FUJII, N .

STUDIA MATHEMATICA, 1991, 98 (03) :175-190

[7] Product rule and chain rule estimates for fractional derivatives on spaces that satisfy the doubling condition [J].

Gatto, AE .

JOURNAL OF FUNCTIONAL ANALYSIS, 2002, 188 (01) :27-37

[8] Interpolation properties of Besov spaces defined on metric spaces [J].

Gogatishvili, Amiran ;

Koskela, Pekka ;

Shanmugalingam, Nageswari .

MATHEMATISCHE NACHRICHTEN, 2010, 283 (02) :215-231

[9] VECTOR-VALUED SINGULAR INTEGRALS AND MAXIMAL FUNCTIONS ON SPACES OF HOMOGENEOUS TYPE [J].

Grafakos, Loukas ;

Liu, Liguang ;

Yang, Dachun .

MATHEMATICA SCANDINAVICA, 2009, 104 (02) :296-310

[10]

Hajasz P, 2003, CONT MATH, V338, P173

← 1 2 3 →