The sharp bound for the Hilbert transform on weighted Lebesgue spaces in terms of the classical Ap characteristic

We show that the norm of the Hilbert transform as an operator in the weighted space L-R(P)(omega) for 2 <= p < infinity is bounded by a constant multiple of the first power of the classical A(p) characteristic of omega. This result is sharp. We also prove a bilinear imbedding theorem with simple conditions.