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We prove a multilinear version of the reverse Hölder inequality in the theory of MuckenhouptA  p{A_{p}}    weights. We give two applications of this inequality to the study of multilinear weighted norm inequalities. First, we prove a structure theorem for multilinearA   p  →{A_{\vec{p}}}    weights; second, we give a new sufficient condition for multilinear, two-weighted norm inequalities for a maximal operator.

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