Title: Maximal functions and Calderon-Zygmund theory for vector-valued functions with operator weights

Authors: Michael Lauzon

Issue: Volume 56 (2007), Issue 4, 1723-1748

Abstract: 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.