A multilinear reverse Holder inequality with applications to multilinear weighted norm inequalities

We prove a multilinear version of the reverse Holder inequality in the theory of Muckenhoupt A(p) weights. We give two applications of this inequality to the study of multilinear weighted norm inequalities. First, we prove a structure theoremformultilinear A((p) over right arrow) weights; second, we give a new sufficient condition for multilinear, two-weighted norm inequalities for a maximal operator.