Interpolation inequalities for modified Sobolev spaces and their implications to inversion of Radon transform

Abstract

The implications of interpolation inequality for Hilbert scales for obtaining estimates for the worst case error for ill-posed problems are well known. In this paper, we prove interpolation inequalities for the modified Sobolev scales, the general form of which was introduced by Sharafutdinov (Inverse Problems 33:025002, 2017), and make use of them along with the recently obtained modified Reshetnyak formulas for Radon transform to obtain error estimates for the worst case error associated with the Radon transform and appropriate source sets.