Semi-Fredholm theory for Wiener-Hopf-Hankel operators on Muckenhoupt weighted Lebesgue spaces

Abstract

We obtain conditions for describing semi-Fredholm properties of Wiener-Hopf plus and minus Hankel operators with semi-almost periodic symbols on weighted Lebesgue spaces $L^p(\mathbb{R}_+, w)$, where $w$ belongs to a subclass of Muckenhoupt weights (and $1<p<\infty$). These conditions are based on the mean values of the representatives at infinity of the Fourier symbols of the Wiener-Hopf and Hankel operators. At the end, three concrete examples to illustrate the theory are given.