Besov Spaces for the Schrödinger Operator with Barrier Potential
Complex Analysis and Operator Theory
Let H = −d 2/dx 2 + V be a Schrödinger operator on the real line, where V=cχ[a,b] , c > 0. We define the Besov spaces for H by developing the associated Littlewood–Paley theory. This theory depends on the decay estimates of the spectral operator φj(H) for the high and low energies. We also prove a Mihlin multiplier theorem on these spaces, including the Lp boundedness result. Our approach has potential applications to other Schrödinger operators with short-range potentials.
Benedetto, John J., Shijun Zheng.
"Besov Spaces for the Schrödinger Operator with Barrier Potential."
Complex Analysis and Operator Theory, 4 (4): 777-811: Birkhäuser.