A non-differentiability result for the inversion operator between Sobolev spaces

The order of differentiability of the inversion operator T between certain spaces or manifolds of distributionally differentiable functions is shown t o be sharp in the following sense. Up to a certain order k guaranted by inv erse function arguments, the operator T is everywhere differentiable and T- (k) is continuous. On the other hand, T is nowhere k + 1 times differentiab le.