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
收藏
页码：1345 / 1366
页数：22
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