Toeplitz operators with PQC symbols on weighted Hardy spaces

We prove a Fredholm criterion for Toeplitz operators with piecewise quasicontinuous symbols on weighted Hardy spaces, thus uniting part of the Gohberg-Krupnik and Sarason theories. The criterion established solved the problem of describing all the subsets M of (1, ∞) with the following property: there exists a Toeplitz operator which is Fredholm on H p if and only if p belongs to M .