Maximal functions and Calderon-Zygmund theory for vector-valued functions with operator weights Michael Lauzon 47G1044A15Calderon-Zygmund decompositionMuckenhoupt weightsweighted spacesvector-valued functions We generalize the Hardy-Littlewood maximal functions to vector-valued functions taking values in a Banach space with a varying weight, $t \mapsto \rho_t$, which satisfies a reverse H\"older condition, and prove estimates on the bounds of the maximal function. We also prove the existence of a Calderon-Zygmund decomposition for functions in $L^p$ ($t \mapsto \rho_t$) when the weight satisfies a reverse H\"older inequality. This decomposition is used to prove an extrapolation theorem for the martingale transform on weighted spaces. Indiana University Mathematics Journal 2007 text pdf 10.1512/iumj.2007.56.2916 10.1512/iumj.2007.56.2916 en Indiana Univ. Math. J. 56 (2007) 1723 - 1748 state-of-the-art mathematics http://iumj.org/access/