Interpolation orbits and optimal Sobolev's embeddings

摘要

We consider Sobolev's embeddings for spaces based on rearrangement invariant spaces (not necessarily with the Fatou property) on domains with a sufficiently smooth boundary in R-n. We show that each optimal embedding W-m E subset of G, where m < n, can be obtained by the real interpolation of the well-known endpoint embeddings. We also give an orbital description of the optimal range space in Sobolev's embedding. (c) 2007 Elsevier Inc. All rights reserved.