Boundedness of spectral multipliers for Schrödinger operators on open sets

Tsukasa Iwabuchi, Tokio Matsuyama, Koichi Taniguchi

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

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-Lqestimates 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.

Original languageEnglish
Pages (from-to)1277-1322
Number of pages46
JournalRevista Matematica Iberoamericana
Volume34
Issue number3
DOIs
Publication statusPublished - 2018 Jan 1

Keywords

  • Functional calculus
  • Kato class
  • Schrödinger operators

ASJC Scopus subject areas

  • Mathematics(all)

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