Boundedness of spectral multipliers for Schrödinger operators on open sets

  • Tsukasa Iwabuchi

    Tohoku University, Sendai, Japan
  • Tokio Matsuyama

    Chuo University, Tokyo, Japan
  • Koichi Taniguchi

    Chuo University, Tokyo, Japan
Boundedness of spectral multipliers for Schrödinger operators on open sets cover
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Abstract

Let HVH_V be a self-adjoint extension of the Schrödinger operator Δ+V(x)-\Delta+V(x) with the Dirichlet boundary condition on an arbitrary open set~Ω\Omega of~Rd\mathbb R^d, where d1d \ge 1 and the negative part of potential VV belongs to the Kato class on Ω\Omega. The purpose of this paper is to prove LpL^p-LqL^q-estimates and gradient estimates for an operator φ(HV)\varphi(H_V), where φ\varphi is an arbitrary rapidly decreasing function on R\mathbb{R}, and φ(HV)\varphi(H_V) is defined via the spectral theorem.

Cite this article

Tsukasa Iwabuchi, Tokio Matsuyama, Koichi Taniguchi, Boundedness of spectral multipliers for Schrödinger operators on open sets. Rev. Mat. Iberoam. 34 (2018), no. 3, pp. 1277–1322

DOI 10.4171/RMI/1024