Non-homogeneous Tb theorem and random dyadic cubes on metric measure spaces

Details Non-homogeneous Tb theorem and random dyadic cubes on metric measure spaces Non-homogeneous Tb theorem and random dyadic cubes on metric measure spaces

2009-11-23

arxiv.org/abs/0911.4387v1

Mathematics

Functional Analysis

34 pages

Scientific paper

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.

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