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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A compact embedding of a Sobolev space is equivalent to an embedding into a better space


Authors: Piotr Hajłasz and Zhuomin Liu
Journal: Proc. Amer. Math. Soc. 138 (2010), 3257-3266
MSC (2010): Primary 46E35; Secondary 46E30
Published electronically: April 15, 2010
MathSciNet review: 2653955
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Abstract: We prove that the compact embedding of the Orlicz-Sobolev space is equivalent to the existence of a bounded embedding into a higher Orlicz space.


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Additional Information

Piotr Hajłasz
Affiliation: Department of Mathematics, University of Pittsburgh, 301 Thackeray Hall, Pittsburgh, Pennsylvania 15260
Email: hajlasz@pitt.edu

Zhuomin Liu
Affiliation: Department of Mathematics, University of Pittsburgh, 301 Thackeray Hall, Pittsburgh, Pennsylvania 15260
Email: liuzhuomin@hotmail.com

DOI: http://dx.doi.org/10.1090/S0002-9939-10-10390-6
PII: S 0002-9939(10)10390-6
Received by editor(s): March 17, 2009
Received by editor(s) in revised form: December 18, 2009
Published electronically: April 15, 2010
Additional Notes: The first author was supported by NSF grants DMS-0500966 and DMS-0900871.
Communicated by: Nigel J. Kalton
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.