On multilinear Littlewood-Paley operators

被引：22

作者：

Chen, Xi ^{[1
,2
]}

Xue, Qingying ^{[1
]}

Yabuta, Kozo ^{[3
]}

机构：

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

[2] Australian Natl Univ, Inst Math Sci, Canberra, ACT 0200, Australia

[3] Kwansei Gakuin Univ, Math Sci Res Ctr, Sanda 6691337, Japan

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2015年 / 115卷

基金：

日本学术振兴会;

关键词：

Multiple weights A(p); Multilinear Marcinkiewicz integral; Multilinear area integral of Lusin; Homogeneous kernels; WEIGHTED NORM INEQUALITIES; L-P-BOUNDEDNESS; SINGULAR-INTEGRALS; COMMUTATORS; L2;

D O I：

10.1016/j.na.2014.12.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we established the weighted estimates for the multilinear Littlewood-Paley operators, including the multilinear Marcinkiewicz integral and the multilinear area integral of Lusin. These operators are generalizations of the linear operators for higher dimension which were first defined and studied by E.M. Stein in 1958. Strong L-p1(omega(1)) x . . . x L-pm(omega(m)) -> L-p(v (omega) over right arrow) estimates when each p(i) > 1 and weak type L-p1(omega(1)) x . . . x L-pm(omega(m)) -> L-p,L-infinity(v (omega) over right arrow) estimates if there is a p(i) = 1 are obtained, where v (omega) over right arrow = Pi(m)(i=1) omega(i) (p/pi) and each w(i)(i = 1, . . . , m) is a nonnegative function on R-n. (C) 2014 Elsevier Ltd. All rights reserved.

引用

页码：25 / 40

页数：16

共 35 条

[1] Weighted Multilinear Square Function Bounds [J].