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

摘要

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.