Sparse domination on non-homogeneous spaces with an application to Ap weights

Abstract

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(1, 1/(p − 1)) of the Ap characteristic of the weight.