Maximal operator for multilinear singular integrals with non-smooth kernels. (English) Zbl 1205.42013

Duong, Xuan Thinh; Ruming; Grafakos, Loukas; Li, Ji; Yan, Lixin

Indiana Univ. Math. J. 58, No. 6, 2517-2542 (2009).

The authors establish the Cotlar’s inequality for the maximal singular integral operators associated with \(m\)-linear operators whose kernels satisfy regularity conditions that are significantly weaker than those of the standard Calderón-Zygmund kernels. By using this inequality, they obtain multilinear weighted norm inequalities for these operators. As application, they give the weighted norm inequalities of the maximal \(m\)-th order Calderón commutators.

Reviewer: Pu Zhang (Mudanjiang)

MSC:

42B20	Singular and oscillatory integrals (Calderón-Zygmund, etc.)
42B25	Maximal functions, Littlewood-Paley theory
47G30	Pseudodifferential operators

Keywords:

multilinear singular integrals; maximal operator; Cotlar’s inequality; weighted norm inequalities; generalized Calderón-Zygmund operators; commutators; non-smooth kernel