On singular integral equations with the Carleman shifts in the case of the vanishing coefficient (Q1431400)

The paper deals with the solvability for a class of singular integral equations with Carleman shift (generated by linear-fractional functions) on the unit circle \(\Gamma\) in the case when one of the coefficients vanishes on the circle. The main result states that the equation under consideration has a solution in the space of Hölder functions if and only if some singular integral equation (without shift) has a solution with additional properties. The paper contains some errors (or, probably, inaccuracies). For example, the authors write the equality of the following type: \((S\varphi)(z_{0})=\Phi^{-}(z_{0})\) where \(S\) and \(\Phi^{-}\) have the standard sense in the theory of boundary value problems, \(\varphi\) is a function on \(\Gamma\) satisfying the Hölder condition and \(| z_{0}| >1\) (page 332).