Riesz potentials in Besov and Triebel-Lizorkin spaces over spaces of homogeneous type

被引：9

作者：

Yang, DC ^{[1
]}

机构：

[1] Beijing Normal Univ, Dept Math, Beijing 100875, Peoples R China

来源：

POTENTIAL ANALYSIS | 2003年 / 19卷 / 02期

关键词：

space of homogeneous type; Riesz potential; Besov space; Triebel-Lizorkin space;

D O I：

10.1023/A:1023217617339

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

By using the discrete Calderon reproducing formulae, the author first establishes the boundedness of the Riesz-potential-type operator in homogeneous Besov and Triebel-Lizorkin spaces over spaces of homogeneous type. Then, by use of the T1 theorems for these spaces, the author proves that this operator of Riesz potential type can be used as the lifting operator of these spaces.

引用

页码：193 / 210

页数：18

共 20 条

[1]

Christ M., 1990, Colloq. Math, V60, P601, DOI [10.4064/cm-60-61-2-601-628, DOI 10.4064/CM-60-61-2-601-628]

[2]

Coifman RR., 1971, Lect. Notes Math., DOI 10.1007/BFb0058946

[3]

Davis W C, 1985, Prog Vet Microbiol Immunol, V1, P1

[4]

DENG D, T1 THEOREMS BESOV TR

[5] SOME MAXIMAL INEQUALITIES [J].

FEFFERMAN, C ;

STEIN, EM .

AMERICAN JOURNAL OF MATHEMATICS, 1971, 93 (01) :107-+

[6]

Gatto AE, 1999, STUD MATH, V133, P19

[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] On fractional differentiation and integration on spaces of homogeneous type [J].

Gatto, AE ;

Segovia, C ;

Vagi, S .

REVISTA MATEMATICA IBEROAMERICANA, 1996, 12 (01) :111-145

[9]

Han Y., 2002, DISS MATH, V403, P1, DOI DOI 10.4064/dm403-0-1

[10]

HAN Y, SOME NEW BESOV TRIEB

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