We prove a quadratic sparse domination result for general non-integral square functions S. That is, we prove an estimate of the formwhere q * 0 is the Hölder conjugate of q 0 /2, M is the underlying doubling space and S is a sparse collection of cubes on M . Our result will cover both square functions associated with divergence form elliptic operators and those associated with the Laplace-Beltrami operator. This sparse domination allows us to derive optimal norm estimates in the weighted space L p (w).2010 Mathematics Subject Classification. 42B20, 42B37.

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