Sharp Lp estimates for Schrödinger groups

• Piero D'Ancona ^[2] ; Fabio Nicola ^[1]
  1. [1] Polytechnic University of Turin

     Polytechnic University of Turin

     Torino, Italia

     
  2. [2] Università di Roma La Sapienza
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 32, Nº 3, 2016, págs. 1019-1038
• Idioma: inglés
• DOI: 10.4171/RMI/907
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.