Systems of dyadic cubes in a doubling metric space

Tuomas Hytönen, and Anna Kairema. "Systems of dyadic cubes in a doubling metric space." Colloquium Mathematicae 126.1 (2012): 1-33. <http://eudml.org/doc/286231>.

@article{TuomasHytönen2012,
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.},
author = {Tuomas Hytönen, Anna Kairema},
journal = {Colloquium Mathematicae},
keywords = {space of homogeneous type; dyadic cube; random geometric construction},
language = {eng},
number = {1},
pages = {1-33},
title = {Systems of dyadic cubes in a doubling metric space},
url = {http://eudml.org/doc/286231},
volume = {126},
year = {2012},
}

TY - JOUR
AU - Tuomas Hytönen
AU - Anna Kairema
TI - Systems of dyadic cubes in a doubling metric space
JO - Colloquium Mathematicae
PY - 2012
VL - 126
IS - 1
SP - 1
EP - 33
AB - 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.
LA - eng
KW - space of homogeneous type; dyadic cube; random geometric construction
UR - http://eudml.org/doc/286231
ER -