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A remark on Calderón-Zygmund classes and Sobolev spaces


Author: David Swanson
Journal: Proc. Amer. Math. Soc. 130 (2002), 1655-1659
MSC (2000): Primary 46E35
Published electronically: January 28, 2002
MathSciNet review: 1887038
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Abstract: We show how the Sobolev space $W^{k,p}(\mathbf{R}^n)$ may be characterized in terms of the local behavior of its members. We use the local $T^{k,p}$-classes introduced by Calderón and Zygmund.


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Additional Information

David Swanson
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
Email: dswanson@math.tamu.edu

DOI: https://doi.org/10.1090/S0002-9939-02-06458-4
Keywords: Sobolev spaces, Calder\'{o}n-Zygmund classes
Received by editor(s): October 2, 2000
Published electronically: January 28, 2002
Communicated by: David Preiss
Article copyright: © Copyright 2002 American Mathematical Society