  Properties of a maximal function for vector-valued martingales were studied
by the author in an earlier paper. Restricting here to the dyadic setting, we
prove the equivalence between (weighted) L^p inequalities and weak type
estimates, and discuss an extension to the case of locally finite Borel
measures on R^n. In addition, to compensate for the lack of an L^\infty
inequality, we derive a suitable BMO estimate. Different dyadic systems in
different dimensions are also considered.
