Wiener-Hopf Operators with Semi-almost Periodic Matrix Symbols on Weighted Lebesgue Spaces

Abstract

Fredholm criteria and index formulas are established for Wiener-Hopf operators W(a) with semi-almost periodic matrix symbols a on weighted Lebesgue spaces $$L^{p}_{N}({\mathbb{R}}_{+},w)$$ where 1 < p < ∞, w belongs to a subclass of Muckenhoupt weights and $$N \in {\mathbb{N}}$$ . We also study the invertibility of Wiener-Hopf operators with almost periodic matrix symbols on $$L^{p}_{N}({\mathbb{R}}_{+},w)$$ . In the case N = 1 we also obtain a semi-Fredholm criterion for Wiener-Hopf operators with semi-almost periodic symbols and, for another subclass of weights, a Fredholm criterion for Wiener-Hopf operators with semi-periodic symbols.