On commutators of Marcinkiewicz integrals with rough kernel

被引：72
|
作者：
Ding, Y [1 ]
Lu, SZ
Yabuta, K
机构：
[1] Beijing Normal Univ, Dept Math, Beijing 100875, Peoples R China
[2] Kwansei Gakuin Univ, Sch Sci, Sanda 6691337, Japan
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2002年 / 275卷 / 01期
关键词：
Marcinkiewicz integral; Littlewood-Paley function; commutator; rough kernel; A(p) weight;
D O I：
10.1016/S0022-247X(02)00230-5
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this note we prove that the higher-order commutators mu(Omega,b)(m), mu(Omega,lambda,b)(*m) and mu(Omega,S,b)(m) are all of bounded operators on the weighted L-P spaces. These commutators are formed respectively by a BMO(R-n) function b(x) and a class of rough Marcinkiewicz integral mu(Omega), mu(Omega,lambda)(*) and mu(Omega,S), which are corresponding to the Littlewood-Paley g-function, Littlewood-Paley g(lambda)(*)-function and the Lusin area integral, respectively. The results in this paper are essential improvements and extensions of the results by Torchinsky and Wang (1990) and by Alvarez et al. (1993). (C) 2002 Elsevier Science (USA). All rights reserved.
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页码：60 / 68
页数：9
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