Systems of dyadic cubes in a doubling metric space

• Autorzy: Tuomas Hytönen , Anna Kairema
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 60D05: Geometric probability and stochastic geometry
• 42B25: Maximal functions, Littlewood-Paley theory
• 30L99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2012
• Tom: 126
• Numer: 1
• Strony: 1-33

Daty

wydano

2012

Twórcy

autor

Tuomas Hytönen

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

autor

Anna Kairema

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

Identyfikatory

DOI

10.4064/cm126-1-1