%0 Journal Article
%T Non-homogeneous Tb theorem and random dyadic cubes on metric measure spaces
%A Tuomas Hyt£¿nen
%A Henri Martikainen
%J Mathematics
%D 2009
%I arXiv
%X We prove a Tb theorem on quasimetric spaces equipped with what we call an upper doubling measure. This is a property that encompasses both the doubling measures and those satisfying the upper power bound \mu(B(x,r)) \le Cr^d. Our spaces are only assumed to satisfy the geometric doubling property: every ball of radius r can be covered by at most N balls of radius r/2. A key ingredient is the construction of random systems of dyadic cubes in such spaces.
%U http://arxiv.org/abs/0911.4387v1