Resumen de Sharp Lp estimates for Schrödinger groups on spaces of homogeneous type

The Anh Bui, Piero D'Ancona , Fabio Nicola

• We prove an Lp estimate ∥e−itLφ(L)f∥p≲(1+|t|)s∥f∥p,t∈R,s=n∣∣12−1p∣∣ for the Schrödinger group generated by a semibounded, self-adjoint operator L on a metric measure space X of homogeneous type (where n is the doubling dimension of X). The assumptions on L are a mild Lp0→Lp′0 smoothing estimate and a mild L2→L2 off-diagonal estimate for the corresponding heat kernel e−tL. The estimate is uniform for φ varying in bounded sets of S(R),or more generally of a suitable weighted Sobolev space.