A criterion for the weighted Cauchy singular operator to belong to the algebra of singular integral operators with coefficients in a Sarason algebra (Q1907463)

Let \(S_{p\omega}\) be the singular Cauchy operator acting in the weighted Lebesgue space \(L_p(T, \omega(t)|dt|)\) \((1< p< \infty)\), where \(\{T: |t|= 1\}\) and \(\omega\) is a weight function. A criterion for the singular operators \[ \alpha_{\omega} (S_{p\omega})= N_{\omega^{\frac 1p}} S_{p\omega} N_{\omega^{\frac 1p}}^{- 1} \] (\(N_{\frac 1p}\) is the operator of multiplication by \(\omega^{\frac 1p}\)) to belong to the algebra of singular operators with coefficients in a Sarason algebra is given.