Commutators of Marcinkiewicz integral with rough kernels on Sobolev spaces

被引：2

作者：

Chen, Yan Ping ^{[2
]}

Ding, Yong ^{[1
]}

Wang, Xin Xia ^{[3
]}

机构：

[1] Beijing Normal Univ, Sch Math Sci, Lab Math & Complex Syst BNU, Minist Educ, Beijing 100875, Peoples R China

[2] Univ Sci & Technol Beijing, Dept Math & Mech, Sch Appl Sci, Beijing 100083, Peoples R China

[3] Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830046, Peoples R China

来源：

ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2011年 / 27卷 / 07期

基金：

中国国家自然科学基金;

关键词：

Marcinkiewicz integral; commutator; rough kernel; Sobolev space; Bony paraproduct; SINGULAR KERNELS; BOUNDEDNESS; OPERATORS;

D O I：

10.1007/s10114-011-8544-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the authors give the boundedness of the commutator [b, mu(Omega,gamma)] from the homogeneous Sobolev space. L(gamma)(p)(R(n)) to the Lebesgue space L(p)(R(n)) for 1 < p < infinity, where mu(Omega,gamma). denotes the Marcinkiewicz integral with rough hypersingular kernel defined by [GRAPHICS] with Omega is an element of L(1) (S(n-1)) for 0 < gamma < min {n/2, n/p} or Omega is an element of L(log(+) L)(beta) (S(n-1)) for vertical bar 1 - 2/p vertical bar < beta < 1 (0 < gamma < n/2), respectively.

引用

页码：1345 / 1366

页数：22

共 16 条

[1]

Al-Salman A, 2002, MATH RES LETT, V9, P697

[2] Operators with rough singular kernels [J].

Chen, Daning ;

Ding, Yong ;

Fan, Dashan .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 337 (02) :906-918

[3] Certain operators with rough singular kernels [J].

Chen, JC ;

Fan, DS ;

Ying, YM .

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2003, 55 (03) :504-532

[4] Boundedness of commutators of Marcinkiewicz integral with rough variable kernel [J].

Chen, Yanping ;

Ding, Yong .

INTEGRAL EQUATIONS AND OPERATOR THEORY, 2008, 61 (04) :477-492

[5] Lp-boundedness of Marcinkiewicz integrals with Hardy space function kernels [J].

Ding, Y ;

Fan, DS ;

Pan, YB .

ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2000, 16 (04) :593-600

[6] On commutators of Marcinkiewicz integrals with rough kernel [J].

Ding, Y ;

Lu, SZ ;

Yabuta, K .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2002, 275 (01) :60-68

[7] L2-BOUNDEDNESS OF A SINGULAR INTEGRAL OPERATOR [J].

Fan, Dashan ;

Pan, Yibiao .

PUBLICACIONS MATEMATIQUES, 1997, 41 (02) :317-333

[8]

FRAZIER M, 1988, LECT NOTES MATH, V1302, P223

[9]

Grafakos L., 2004, Classical and Modern Fourier Analysis

[10] Lp(Rn) boundedness for the commutator of a homogeneous singular integral operator [J].

Hu, G .

STUDIA MATHEMATICA, 2003, 154 (01) :13-27

← 1 2 →