Systems of dyadic cubes in a doubling metric space
Volume 126 / 2012
Colloquium Mathematicum 126 (2012), 1-33
MSC: Primary 30L99; Secondary 42B25, 60D05.
DOI: 10.4064/cm126-1-1
Abstract
A number of recent results in Euclidean harmonic analysis have exploited several adjacent systems of dyadic cubes, instead of just one fixed system. In this paper, we extend such constructions to general spaces of homogeneous type, making these tools available for analysis on metric spaces. The results include a new (non-random) construction of boundedly many adjacent dyadic systems with useful covering properties, and a streamlined version of the random construction recently devised by H. Martikainen and the first author. We illustrate the usefulness of these constructions with applications to weighted inequalities and the BMO space; further applications will appear in forthcoming work.
