Resumen de Sharp Lp estimates for Schrödinger groups

Piero D'Ancona , Fabio Nicola

• Consider a non-negative self-adjoint operator H in L2(Rd). We suppose that its heat operator e−tHe satisfies an off-diagonal algebraic decay estimate, for some exponents p0∈[0,2]. Then we prove sharp Lp→Lp frequency truncated estimates for the Schrödinger group eitH for p∈[p0,p′0].

  In particular, our results apply to every operator of the form H=(i∇+A)2+V, with a magnetic potential A∈L2loc(Rd,Rd) and an electric potential V whose positive and negative parts are in the local Kato class and in the Kato class, respectively.