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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
DOI: https://doi.org/10.1090/S0002-9939-02-06458-4
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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  • [AH] Adams, D. R., and Hedberg, L. I., Function Spaces and Potential Theory, Grundlehren der Mathematischen Wissenschaften, Springer, 1996. MR 97j:46024
  • [BZ] Bagby, T., and Ziemer, W. P., Pointwise differentiability and absolute continuity, Trans. Amer. Math. Soc. 194 (1974), 129-148. MR 49:9129
  • [BH] Bojarski, B., and Haj\lasz, P., Pointwise inequalities for Sobolev functions and some applications, Studia Math. 106 (1) 1993, 77-92. MR 94h:46045
  • [C] Calderón, A. P., Uniqueness of distributions, Unión Mate. Argentina 25 (1970), 37-55. MR 49:7762
  • [CZ] Calderón, A. P., and Zygmund, A., Local properties of solutions to elliptic partial differential equations, Studia Math. 20 (1960), 171-225. MR 25:310
  • [H] Haj\lasz, P., Sobolev spaces on an arbitrary metric space, Pot. Anal. 5 (1996), 403-415. MR 97f:46050
  • [S] Strichartz, R. S., Multipliers on fractional Sobolev spaces, J. Math. Mech. 16 (1967), 1031-1060. MR 35:5927
  • [Z] Ziemer, W. P., Weakly Differentiable Functions, GTM 120, Springer-Verlag, 1989. MR 91e:46046

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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

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