Mourre's commutator method is used together with Besov spaces, in this paper, to settle the question of uniqueness of solutions to the scattering problem for the acoustic wave propagation in perturbed stratified fluids in Rn with n [ges ] 2: The uniqueness of solutions is established by introducing a radiation condition in the framework of Besov spaces, and is then used to prove resolvent estimates in the Besov space setting for the acoustic propagator in perturbed stratified fluids. These estimates are ‘sharp’ in a sense made precise in the text and are important in establishing existence of solutions to the scattering problem.