Large-scale equivalence of norms of Radon transform and initial function

The purpose of the topic of the article in the future is to establish the equivalence in their norms of the problems of recovery the Computed Tomography and the Computational (numerical) diameter (C(N)D), which was in 2019 previously performed in the case of functions of two variables. And this was based on the equivalence of the corresponding norms proved by Frank Natterer in the same two-dimensional Sobolev spaces. In this article, for the case of functions of any dimension, a large-scale equivalence in its norm of the Radon transform and the function that generated it is established.