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

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 (L-v(w) over arrow(q), L-p)(alpha) (R-n). Some criterions of boundedness for such operators in (L-v(w) over arrow(q), L-p)(alpha) (R-n) are given. As applications, the norm inequalities for the multilinear Calderon-Zygmund operators and multilinear singular integrals with nonsmooth kernels as well as the corresponding commutators on (L-v(w) over arrow(q), L-p)(alpha) (R-n) are obtained.