Dyadic Fefferman-Stein Inequalities and the Equivalence of Haar Bases on Weighted Lebesgue Spaces

Abstract

In this note we give conditions on two dyadic systems to obtain the equivalence of corresponding Haar systems on dyadic weighted Lebesgue spaces on spaces of homogeneous type. In order to obtain these result we prove a Fefferman-Stein weighted inequality for vector valued dyadic Hardy-
Littlewood maximal operators with dyadic weights in this general setting.