The Sharp Weighted Bound for Multilinear Maximal Functions and Caldern-Zygmund Operators

We investigate the weighted bounds for multilinear maximal functions and Calderon-Zygmund operators from L-p1(w(1)) x ... x L-pm(w(m)) to L-p(v(w)over right arrow, w), where 1 < p(1), ... , p(m) < infinity with 1/p(1) + .... + 1/p(m) = 1/p and (w)over right arrow w is a multiple A(p)over right arrow weight. We prove the sharp bound for the multilinear maximal function for all such p1,..., pm and prove the sharp bound for m-linear Calderon-Zymund operators when p >= 1.