Sharp Sobolev type embeddings on the entire Euclidean space
Functional Analysis
2017-12-01 v1
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.
Cite
@article{arxiv.1711.11549,
title = {Sharp Sobolev type embeddings on the entire Euclidean space},
author = {Angela Alberico and Andrea Cianchi and Lubos Pick and Lenka Slavikova},
journal= {arXiv preprint arXiv:1711.11549},
year = {2017}
}