On multilinear Littlewood–Paley operators. (March 2015) - Chen, Xi; Xue, Qingying; Yabuta, Kôzô
Abstract: 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 p 1 ( ω 1 ) × ⋯ × L p m ( ω m ) ⟶ L p ( ν ω → ) estimates when each p i > 1 and weak type L p 1 ( ω 1 ) × ⋯ × L p m ( ω m ) ⟶ L p, ∞ ( ν ω → ) estimates if there is a p i = 1 are obtained, where ν ω → = ∏ i = 1 m ω i p p i and each w i ( i = 1, …, m ) is a nonnegative function on R n .