Fredholm Theory for a Class of Singular Integral Operators with Carleman Shift and Unbounded Coefficients

Abstract

Abstract A criterion for the Fredholmness of singular integral operators with Carleman shift in L P (Γ ) is obtained, where Γ is either the unit circle or the real line. The approach allows to consider unbounded coefficients in a class related to that of quasicontinuous functions. Applications to Wiener‐Hopf‐Hankel type operators and operators with linear fractional Carleman shift on IR are included.