Discrete Wiener-Hopf operators on spaces with Muckenhoupt weight

The discrete Wiener-Hopf operator generated by a function a(e(i theta)) wit h the Fourier series Sigma (n is an element ofZ)a(n)e(in theta) is the oper ator T(a) induced by the Toeplitz matrix (a(j-k))(j,k=0)(infinity) on some weighted sequence space l(p)(Z(+), w). We assume that w satisfies the Mucke nhoupt A(p) condition and that a is a piecewise continuous function subject to some natural multiplier condition. The last condition is in particular satisfied if a is of bounded variation. Our main result is a Fredholm crite rion and an index formula for T(a). It implies that the essential spectrum of T(a) results from the essential range of a by filling in certain horns b etween the endpoints of each jump. The shape of these horns is determined b y the indices of powerlikeness of the weight w.