Transactions of the American Mathematical Society

Author(s): Mario Milman
Journal: Trans. Amer. Math. Soc. 357 (2005), 3425-3442.
MSC (2000): Primary 46E30, 46M35, 26D10
Posted: April 27, 2005
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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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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 46E30, 46M35, 26D10

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

DOI: 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
Posted: April 27, 2005
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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