Publication at Faculty of Mathematics and Physics |
2018
Abstract
A comprehensive approach to Sobolev type embeddings, involving arbitrary rearrangement-invariant norms on the entire Euclidean space R-n, is offered. In particular, the optimal target space in any such embedding is exhibited.
Crucial in our analysis is a new reduction principle for the relevant embeddings, showing their equivalence to a couple of considerably simpler one-dimensional inequalities. Applications to the classes of the Orlicz-Sobolev and the Lorentz-Sobolev spaces are also presented.
These contributions fill in a gap in the existing literature, where sharp results in such a general setting are only available for domains of finite measure.