2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73250Let H be a Schrodinger operator with barrier potential on the real line. 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 in the high and low energies. We also prove a Mikhlin-Hormander type multiplier theorem on these spaces, including the Lp boundedness result. Our approach has potential applications to other Schrodinger operators with short-range potentials, as well as in higher dimensions.35 pagesClassical Analysis and ODEsSpectral Theory42B25; 35P25text