Limiting absorption principle on Lp-spaces and scattering theory

Journal of Mathematical Physics, Volume 61, Issue 9, September 2020. In this paper, we study the mapping property from Lp to Lq of the resolvent of the Fourier multipliers and scattering theory of generalized Schrödinger operators. Although the first half of the subject was studied by Cuenin [J. Funct. Anal. 272(7), 2987–3018 (2017)], we extend their result away from the duality line, and we also study the Hölder continuity of the resolvent.