TY - JOUR
T1 - On multilinear Littlewood-Paley operators
AU - Chen, Xi
AU - Xue, Qingying
AU - Yabuta, Kôzô
N1 - Publisher Copyright:
© 2014 Elsevier Ltd. All rights reserved.
PY - 2015/2
Y1 - 2015/2
N2 - 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 Lp1(ω1)×⋯×Lpm(ωm)→Lp(νω→) estimates when each pi>1 and weak type Lp1(ω1)×⋯×Lpm(ωm)→Lp,∞(νω→) estimates if there is a pi=1 are obtained, where νω→=i=1mωippi and each wi(i=1,...,m) is a nonnegative function on Rn.
AB - 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 Lp1(ω1)×⋯×Lpm(ωm)→Lp(νω→) estimates when each pi>1 and weak type Lp1(ω1)×⋯×Lpm(ωm)→Lp,∞(νω→) estimates if there is a pi=1 are obtained, where νω→=i=1mωippi and each wi(i=1,...,m) is a nonnegative function on Rn.
KW - Homogeneous kernels
KW - Multilinear Marcinkiewicz integral
KW - Multilinear area integral of Lusin
KW - Multiple weights A
UR - http://www.scopus.com/inward/record.url?scp=84919950576&partnerID=8YFLogxK
U2 - 10.1016/j.na.2014.12.001
DO - 10.1016/j.na.2014.12.001
M3 - Article
SN - 0362-546X
VL - 115
SP - 25
EP - 40
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
ER -