Multilinear Marcinkiewicz-Zygmund inequalities

Abstract

We extend to the multilinear setting classical inequalities of Marcinkiewicz and Zygmund on (Formula presented.)-valued extensions of linear operators. We show that for certain (Formula presented.), there is a constant (Formula presented.) such that for every bounded multilinear operator (Formula presented.) and functions (Formula presented.), the following inequality holds (Formula presented.)In some cases we also calculate the best constant (Formula presented.) satisfying the previous inequality. We apply these results to obtain weighted vector-valued inequalities for multilinear Calderón-Zygmund operators.