Singular Integral Operators with Carleman Shift and Discontinuous Coefficients in the Spaces $H^{\omega}_0(\Gamma,\rho)$

Abstract

For the singular integral operators with Carleman shift, preserving or changing orientation, and piecewise continuous coefficients we prove the theorem on Fredholmness and obtain the formula for index in the generalized Holder spaces \(H^{\omega}_0(\Gamma,\rho)\) defined by an arbitrary continuity modulus ω from the Bari-Stechkin class and some general weights on a closed or open finite Lyapunov curve Γ.