A compact embedding of a Sobolev space is equivalent to an embedding into a better space
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- by Piotr Hajłasz and Zhuomin Liu PDF
- Proc. Amer. Math. Soc. 138 (2010), 3257-3266 Request permission
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.References
- Robert A. Adams and John J. F. Fournier, Sobolev spaces, 2nd ed., Pure and Applied Mathematics (Amsterdam), vol. 140, Elsevier/Academic Press, Amsterdam, 2003. MR 2424078
- Andrea Cianchi, A sharp embedding theorem for Orlicz-Sobolev spaces, Indiana Univ. Math. J. 45 (1996), no. 1, 39–65. MR 1406683, DOI 10.1512/iumj.1996.45.1958
- John B. Conway, A course in functional analysis, 2nd ed., Graduate Texts in Mathematics, vol. 96, Springer-Verlag, New York, 1990. MR 1070713
- Claude Dellacherie and Paul-André Meyer, Probabilities and potential, North-Holland Mathematics Studies, vol. 29, North-Holland Publishing Co., Amsterdam-New York, 1978. MR 521810
- Piotr Hajłasz and Pekka Koskela, Isoperimetric inequalities and imbedding theorems in irregular domains, J. London Math. Soc. (2) 58 (1998), no. 2, 425–450. MR 1668136, DOI 10.1112/S0024610798006346
- Agnieszka Kałamajska, On compactness of embedding for Sobolev spaces defined on metric spaces, Ann. Acad. Sci. Fenn. Math. 24 (1999), no. 1, 123–132. MR 1677969
- Ron Kerman and Luboš Pick, Compactness of Sobolev imbeddings involving rearrangement-invariant norms, Studia Math. 186 (2008), no. 2, 127–160. MR 2407972, DOI 10.4064/sm186-2-2
- Jindřich Nečas, Les méthodes directes en théorie des équations elliptiques, Masson et Cie, Éditeurs, Paris; Academia, Éditeurs, Prague, 1967 (French). MR 0227584
- M. M. Rao and Z. D. Ren, Theory of Orlicz spaces, Monographs and Textbooks in Pure and Applied Mathematics, vol. 146, Marcel Dekker, Inc., New York, 1991. MR 1113700
Additional Information
- Piotr Hajłasz
- Affiliation: Department of Mathematics, University of Pittsburgh, 301 Thackeray Hall, Pittsburgh, Pennsylvania 15260
- MR Author ID: 332316
- Email: hajlasz@pitt.edu
- Zhuomin Liu
- Affiliation: Department of Mathematics, University of Pittsburgh, 301 Thackeray Hall, Pittsburgh, Pennsylvania 15260
- Email: liuzhuomin@hotmail.com
- 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
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 3257-3266
- MSC (2010): Primary 46E35; Secondary 46E30
- DOI: https://doi.org/10.1090/S0002-9939-10-10390-6
- MathSciNet review: 2653955