Some remarks on the dyadic Rademacher maximal function
Volume 131 / 2013
Colloquium Mathematicum 131 (2013), 113-128
MSC: Primary 42B25; Secondary 46E40.
DOI: 10.4064/cm131-1-10
Abstract
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 $\mathbb {R}^n$. In addition, to compensate for the lack of an $L^\infty $ inequality, we derive a suitable $\rm {BMO}$ estimate. Different dyadic systems in different dimensions are also considered.
