Limiting absorption principle on $L^p$-spaces and scattering theory

In this paper, we study the mapping property form $L^p$ to $L^q$ of the resolvent of the Fourier multiplier operators and scattering theory of generalized Schr"odinger operators. Though the first half of the subject is studied in [4], we extend their result to away from the duality line and we also study the H"older continuity of the resolvent.