A normalization problem for a class of singular integral operators with Carleman shift and unbounded coefficients (Q1892624)

The authors consider the normalization problem for singular integral operators with weighted Carleman shift \(U\) and unbounded coefficients: \(R= P_ ++ (aI+ bU)P_ -\), where \(P_ \pm= {1\over 2} (I+ S)\) and \(S\) is the operator of singular integration in \(L_ p(\Gamma)\), \(p> 1\), where \(\Gamma\) is the unit circle or the real axis. They show that the considered problem may be reduced to an analogous normalization problem for singular integral operators with bounded coefficients.