We extend Lerner's recent approach to sparse domination of Calderón–Zygmund operators to upper doubling (but not necessarily doubling), geometrically doubling metric measure spaces. Our domination theorem, different from the one obtained recently by Conde-Alonso and Parcet, yields a weighted estimate with the sharp power max of the characteristic of the weight.
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Alexander Volberg, Pavel Zorin-Kranich, Sparse domination on non-homogeneous spaces with an application to weights. Rev. Mat. Iberoam. 34 (2018), no. 3, pp. 1401–1414DOI 10.4171/RMI/1029