Weighted Sharp Inequality for Vector-Valued Multilinear Integral Operator

In this paper, we prove the sharp inequality for some vector-valued multilinear integral operators. The operators include Littlewood-Paley operators, Marcinkiewicz operators and Bochner-Riesz operator. By using this inequality, we obtain the weighted L^p-norm inequality and Llog L-type inequality for the vector-valued multilinear operators.