On Landweber iteration for nonlinear ill-posed problems in Hilbert scales

In this paper we derive convergence rates results for Landweber iteration in Hilbert scales in terms of the iteration index k for exact data and in terms of the noise level δ for perturbed data. These results improve the one obtained recently for Landweber iteration for nonlinear ill-posed problems in Hilbert spaces. The conditions needed to obtain the rates are illustrated for a nonlinear Hammerstein integral equation.