On the Multilinear Singular Integrals and Commutators in the Weighted Amalgam Spaces

Abstract

This paper is concerned with the norm estimates for the multilinear singular integral operators and their commutators formed by BMO functions on the weighted amalgam spaces Lvw→q,Lpαℝn. Some criterions of boundedness for such operators in Lvw→q,Lpαℝn are given. As applications, the norm inequalities for the multilinear Calderón-Zygmund operators and multilinear singular integrals with nonsmooth kernels as well as the corresponding commutators on Lvw→q,Lpαℝn are obtained.