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-N(p)(R+, w) where 1 < p < infinity, w belongs to a subclass of Muckenhoupt weights and N epsilon N. We also study the invertibility of Wiener-Hopf operators with almost periodic matrix symbols on L-N(p)(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.