Publication at Faculty of Mathematics and Physics |
2018
Abstract
A sufficient condition for higher-order compact embeddings on bounded domains in Carnot-Caratheodory spaces is established for the class of rearrangement-invariant function spaces. The condition is expressed in terms of compactness of a suitable 1-dimensional integral operator depending on the isoperimetric function relative to the Carnot-Caratheodory structure of the relevant sets.
The general result is then applied to particular Sobolev spaces built upon Lebesgue and Lorentz spaces.