Besov spaces for Schrodinger operators with barrier potentials

摘要

Let H be a Schrodinger operator with barrier potential on the real line. Wedefine the Besov spaces for H by developing the associated Littlewood-Paleytheory. This theory depends on the decay estimates of the spectral operator inthe high and low energies. We also prove a Mikhlin-Hormander type multipliertheorem on these spaces, including the Lp boundedness result. Our approach haspotential applications to other Schrodinger operators with short-rangepotentials, as well as in higher dimensions.