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

Abstract

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 μ(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.

34 pages

References in corpus (2)

• Bergman-type Singular Operators and the Characterization of Carleson Measures for Besov--Sobolev Spaces on the Complex Ball
• A framework for non-homogeneous analysis on metric spaces, and the RBMO space of Tolsa

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• Random "dyadic" lattice in geometrically doubling metric space and $A_2$ conjecture
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• Non-Homogeneous Local $T1$ Theorem: Dual Exponents
• A T(b) Theorem on Product Spaces
• An Improved Compact Embedding Theorem for Degenerate Sobolev Spaces
• Singular operators with antisymmetric kernels, related capacities, and Wolff potentials