Open Access
October 2018 Higher-order compact embeddings of function spaces on Carnot–Carathéodory spaces
Martin Franců
Banach J. Math. Anal. 12(4): 970-994 (October 2018). DOI: 10.1215/17358787-2018-0003
Abstract

A sufficient condition for higher-order compact embeddings on bounded domains in Carnot–Carathéodory 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–Carathéodory structure of the relevant sets. The general result is then applied to particular Sobolev spaces built upon Lebesgue and Lorentz spaces.

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Copyright © 2018 Tusi Mathematical Research Group
Martin Franců "Higher-order compact embeddings of function spaces on Carnot–Carathéodory spaces," Banach Journal of Mathematical Analysis 12(4), 970-994, (October 2018). https://doi.org/10.1215/17358787-2018-0003
Received: 12 January 2018; Accepted: 25 February 2018; Published: October 2018
Vol.12 • No. 4 • October 2018
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