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 $L^{\Phi }({\mathbb{R}}_{+})$; 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 $X({\mathbb{R}}_{+})$.

22 pages