On multilinear Littlewood–Paley operators. (March 2015)

• Record Type: Journal Article
• Authors: Chen, Xi; Xue, Qingying; Yabuta, Kôzô
• Is Part Of: Nonlinear analysis. Volume 115(2015)
• Page Start: 25
• Page End: 40
• Publication Date: 2015-03
• Subjects: Multiple weights Ap→ -- Multilinear Marcinkiewicz integral -- Multilinear area integral of Lusin -- Homogeneous kernels; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2014.12.001
• Languages: English
• ISSNs: 0362-546X

Abstract

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 .