Banach Journal of Mathematical Analysis

Higher-order compact embeddings of function spaces on Carnot–Carathéodory spaces

Martin Franců

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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.

Article information

Source
Banach J. Math. Anal., Volume 12, Number 4 (2018), 970-994.

Dates
Received: 12 January 2018
Accepted: 25 February 2018
First available in Project Euclid: 30 August 2018

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1535594467

Digital Object Identifier
doi:10.1215/17358787-2018-0003

Mathematical Reviews number (MathSciNet)
MR3858757

Zentralblatt MATH identifier
06946299

Subjects
Primary: 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems
Secondary: 53C17: Sub-Riemannian geometry

Keywords
compact embeddings Carnot–Carathéodory spaces rearrangement-invariant function spaces

Citation

Franců, Martin. Higher-order compact embeddings of function spaces on Carnot–Carathéodory spaces. Banach J. Math. Anal. 12 (2018), no. 4, 970--994. doi:10.1215/17358787-2018-0003. https://projecteuclid.org/euclid.bjma/1535594467


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