Sharp estimates for Schrödinger groups on spaces of homogeneous type

  • The Anh Bui

    Macquarie University, Sydney, Australia
  • Piero D'Ancona

    Università di Roma La Sapienza, Italy
  • Fabio Nicola

    Politecnico di Torino, Italy
Sharp $L^p$ estimates for Schrödinger groups on spaces of homogeneous type cover
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Abstract

We prove an estimate

for the Schrödinger group generated by a semibounded, self-adjoint operator on a metric measure space of homogeneous type (where is the doubling dimension of ). The assumptions on are a mild smoothing estimate and a mild off-diagonal estimate for the corresponding heat kernel . The estimate is uniform for varying in bounded sets of ,or more generally of a suitable weighted Sobolev space.

We also prove, under slightly stronger assumptions on , that the estimate extends to with uniformity also for varying in bounded subsets of . For nonnegative operators uniformity holds for all .

Cite this article

The Anh Bui, Piero D'Ancona, Fabio Nicola, Sharp estimates for Schrödinger groups on spaces of homogeneous type. Rev. Mat. Iberoam. 36 (2020), no. 2, pp. 455–484

DOI 10.4171/RMI/1136