Systems of dyadic cubes in a doubling metric space

Tuomas Hytönen¹ ; Anna Kairema¹

¹ Department of Mathematics and Statistics P.O.B. 68 (Gustaf Hällströmin katu 2) FI-00014 University of Helsinki, Finland

Colloquium Mathematicum, Tome 126 (2012) no. 1, pp. 1-33

Résumé

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.

Détail

DOI : 10.4064/cm126-1-1

Keywords: number recent results euclidean harmonic analysis have exploited several adjacent systems dyadic cubes instead just fixed system paper extend constructions general spaces homogeneous type making these tools available analysis metric spaces results include non random construction boundedly many adjacent dyadic systems useful covering properties streamlined version random construction recently devised nbsp martikainen first author illustrate usefulness these constructions applications weighted inequalities bmo space further applications appear forthcoming work