On multilinear Littlewood–Paley operators

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>1pi>1 and weak type Lp1(ω1)×⋯×Lpm(ωm)⟶Lp,∞(νω→) estimates if there is a pi=1pi=1 are obtained, where νω→=∏i=1mωippi and each wiwi(i=1,…,m)(i=1,…,m) is a nonnegative function on RnRn.