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Limiting absorption principle on $L^p$-spaces and scattering theory (1904.00505v3)

Published 31 Mar 2019 in math.AP and math.SP

Abstract: 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.