We construct the generalized Fourier transforms for the Schrödinger operator with a $C^2$ long-range potential. For the construction we regularize the potential following Hörmander, and solve the associated eikonal equation. Then, using the solution, we derive strong forms of radiation condition bounds for the associated limiting resolvents. These bounds improve formerly known ones, and much simplify the above construction. For proof of these bounds we employ an elementary commutator argument with a second order differential operator as conjugate operator.