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

TL;DR

This paper investigates the mapping properties of resolvent operators on $L^p$ spaces and explores scattering theory for generalized Schrödinger operators, extending previous results and analyzing resolvent continuity.

Contribution

It extends existing $L^p$ resolvent estimates away from the duality line and studies the H"older continuity of the resolvent for generalized Schrödinger operators.

Findings

Extended resolvent estimates beyond the duality line.

Established H"older continuity of the resolvent.

Analyzed scattering theory for generalized Schrödinger operators.

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.