Resumen de Boundedness of spectral multipliers for Schrödinger operators on open sets

Tsukasa Iwabuchi, Tokio Matsuyama, Koichi Taniguchi

• 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.