- journal article metadata
European Mathematical Society Publishing House
2018-08-30 23:30:01
Revista Matemática Iberoamericana
Rev. Mat. Iberoamericana
RMI
0213-2230
2235-0616
General
10.4171/RMI
http://www.ems-ph.org/doi/10.4171/RMI
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2012)
34
2018
3
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
Schrödinger operators, functional calculus, Kato class
Let $H_V$ be a self-adjoint extension of the Schrödinger operator $-\Delta+V(x)$ with the Dirichlet boundary condition on an arbitrary open set~$\Omega$ of~$\mathbb R^d$, where $d \ge 1$ and the negative part of potential $V$ belongs to the Kato class on $\Omega$. The purpose of this paper is to prove $L^p$-$L^q$-estimates and gradient estimates for an operator $\varphi(H_V)$, where $\varphi$ is an arbitrary rapidly decreasing function on $\mathbb{R}$, and $\varphi(H_V)$ is defined via the spectral theorem.
Operator theory
Real functions
1277
1322
10.4171/RMI/1024
http://www.ems-ph.org/doi/10.4171/RMI/1024
8
27
2018