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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Notes on limits of Sobolev spaces and the continuity of interpolation scales


Author: Mario Milman
Journal: Trans. Amer. Math. Soc. 357 (2005), 3425-3442
MSC (2000): Primary 46E30, 46M35, 26D10
Published electronically: April 27, 2005
MathSciNet review: 2146631
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Abstract: We extend lemmas by Bourgain-Brezis-Mironescu (2001), and Maz'ya-Shaposhnikova (2002), on limits of Sobolev spaces, to the setting of interpolation scales. This is achieved by means of establishing the continuity of real and complex interpolation scales at the end points. A connection to extrapolation theory is developed, and a new application to limits of Sobolev scales is obtained. We also give a new approach to the problem of how to recognize constant functions via Sobolev conditions.


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Additional Information

Mario Milman
Affiliation: Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, Florida 33431
Email: extrapol@bellsouth.net

DOI: http://dx.doi.org/10.1090/S0002-9947-05-03937-1
PII: S 0002-9947(05)03937-1
Keywords: Sobolev spaces, interpolation scales
Received by editor(s): July 8, 2003
Published electronically: April 27, 2005
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.