Fredholm criteria for Wiener-Hopf operators with continuous symbols acting on some Banach function spaces

Abstract

Let $X(\mathbb{R}_{+})$ be one of the following three Banach function spaces: a Lorentz space $L^{p, q}(\mathbb{R}_{+})$ with $1 < p, q < \infty$; a reflexive Orlicz space $L^Φ(\mathbb{R}_{+})$; or a variable Lebesgue space $L^{p(\cdot)}(\mathbb{R}_{+})$ with variable exponent $p(\cdot)\in \mathcal{B}_{M}(\mathbb{R})$. We extend the Fredholm criteria for Wiener-Hopf operators with continuous symbols on the Lebesgue space $L^{p}(\mathbb{R}_{+})$, $1 < p < \infty$, obtained by Roland Duduchava in the late 1970s, to the space $X(\mathbb{R}_{+})$.