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.
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Henri Martikainen, Vector-valued non-homogeneous <em>Tb</em> theorem on metric measure spaces. Rev. Mat. Iberoam. 28 (2012), no. 4, pp. 961–998DOI 10.4171/RMI/699