Revista Matemática Iberoamericana


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Volume 28, Issue 4, 2012, pp. 961–998
DOI: 10.4171/RMI/699

Published online: 2012-10-14

Vector-valued non-homogeneous Tb theorem on metric measure spaces

Henri Martikainen[1]

(1) University of Helsinki, Finland

We prove a vector-valued non-homogeneous Tb theorem on certain quasimetric spaces equipped with what we call an upper doubling measure. Essentially, we merge recent techniques from the domain and range side of things, achieving a Tb theorem which is quite general with respect to both of them.

Keywords: Calderón–Zygmund operator, non-doubling measure, probabilistic constructions in metric spaces, martingale difference, paraproduct

Martikainen Henri: Vector-valued non-homogeneous Tb theorem on metric measure spaces. Rev. Mat. Iberoamericana 28 (2012), 961-998. doi: 10.4171/RMI/699