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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.

Citation

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Martin Franců. "Higher-order compact embeddings of function spaces on Carnot–Carathéodory spaces." Banach J. Math. Anal. 12 (4) 970 - 994, October 2018. https://doi.org/10.1215/17358787-2018-0003

Information

Received: 12 January 2018; Accepted: 25 February 2018; Published: October 2018
First available in Project Euclid: 30 August 2018

zbMATH: 06946299
MathSciNet: MR3858757
Digital Object Identifier: 10.1215/17358787-2018-0003

Subjects:
Primary: 46E35
Secondary: 53C17

Rights: Copyright © 2018 Tusi Mathematical Research Group

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Vol.12 • No. 4 • October 2018
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