  Let $f$ be a martingale with values in a uniformly $p$-smooth Banach space
and $w$ any positive weight. We show that $\mathbb{E} (f^* \cdot w) \lesssim
\mathbb{E}(S_p f \cdot w^*)$, where $\cdot^*$ is the martingale maximal
operator and $S_p$ is the $\ell^p$ sum of martingale increments.
