  We prove that the operator norm of every Banach space valued Calderon-Zygmund
operator T on the weighted Lebesgue-Bochner space depends linearly on the
Muckenhoupt A_2 characteristic of the weight. In parallel with the proof of the
real-valued case, the proof is based on pointwise dominating every Banach space
valued Calderon-Zygmund operator by a series of positive dyadic shifts. In
common with the real-valued case, the pointwise dyadic domination relies on
Lerner's local oscillation decomposition formula, which we extend from
real-valued functions to Banach space valued functions. The extension of
Lerner's local oscillation decomposition formula is based on a Banach space
valued generalization of the notion of median.
