Compactness properties of Sobolev imbeddings for rearrangement invariant norms
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- by Guillermo P. Curbera and Werner J. Ricker PDF
- Trans. Amer. Math. Soc. 359 (2007), 1471-1484 Request permission
Abstract:
Compactness properties of Sobolev imbeddings are studied within the context of rearrangement invariant norms. Attention is focused on the extremal situation, namely, when the imbedding is considered as defined on its optimal Sobolev domain (with the range space fixed). The techniques are based on recent results which reduce the question of boundedness of the imbedding to boundedness of an associated kernel operator (of just one variable).References
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Additional Information
- Guillermo P. Curbera
- Affiliation: Facultad de Matemáticas, Universidad de Sevilla, Aptdo. 1160, Sevilla 41080, Spain
- MR Author ID: 312355
- Email: curbera@us.es
- Werner J. Ricker
- Affiliation: Math.–Geogr. Fakultät, Katholische Universität Eichstätt–Ingolstadt, D–85072 Eichstätt, Germany
- Email: werner.ricker@ku-eichstaett.de
- Received by editor(s): January 3, 2005
- Published electronically: October 17, 2006
- Additional Notes: The authors gratefully acknowledge the support of the Katholische Universität Eichstätt–Ingolstadt (Germany) and D.G.I. #BFM2003–06335–C03–01 (Spain).
The results of this paper were presented at the 7th International Conference on Harmonic Analysis and Partial Differential Equations, held at El Escorial, Spain, in June 2004. - © Copyright 2006 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 359 (2007), 1471-1484
- MSC (2000): Primary 46E35, 46E30; Secondary 47G10
- DOI: https://doi.org/10.1090/S0002-9947-06-04203-6
- MathSciNet review: 2272134