Boundedness of spectral multipliers for Schrödinger operators on open sets

• Tsukasa Iwabuchi ^[1] ; Tokio Matsuyama ^[2] ; Koichi Taniguchi ^[2]
  1. [1] Tohoku University

     Tohoku University

     Aoba-ku, Japón

     
  2. [2] Chuo University

     Chuo University

     Japón

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 34, Nº 3, 2018, págs. 1277-1322
• Idioma: inglés
• DOI: 10.4171/RMI/1024
• Texto completo no disponible (Saber más ...)
• Resumen

  • Let HV be a self-adjoint extension of the Schrödinger operator −Δ+V(x) with the Dirichlet boundary condition on an arbitrary open set~Ω of~Rd, where d≥1 and the negative part of potential V belongs to the Kato class on Ω. The purpose of this paper is to prove Lp-Lq-estimates and gradient estimates for an operator φ(HV), where φ is an arbitrary rapidly decreasing function on R, and φ(HV) is defined via the spectral theorem.