Decay and regularity for the schrödinger equation

Consider the Schrodinger equation {fx25-1}. The following estimates are proved: (A) IfV≡0 then for any 0≤α 1/2, {fx25-3} (B) If |V(x)|≤C(1+|x|2)−1−δ, δ>0, then (if 0 is neither an eigenvalue nor a resonance of −Δ+V), {fx25-4}.