Available in electronic format
Available in print format		 Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

A remark on Calderón-Zygmund classes and Sobolev spaces

Author(s): David Swanson
Journal: Proc. Amer. Math. Soc. 130 (2002), 1655-1659.
MSC (2000): Primary 46E35
Posted: January 28, 2002
Retrieve article in: PDF DVI PostScript
This article is available free of charge

Abstract | References | Similar articles | Additional information

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.

References:

[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

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 46E35

Retrieve articles in all Journals with MSC (2000): 46E35

Additional Information:

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

DOI: 10.1090/S0002-9939-02-06458-4
PII: S 0002-9939(02)06458-4
Keywords: Sobolev spaces, Calder\'{o}n-Zygmund classes
Received by editor(s): October 2, 2000
Posted: January 28, 2002
Communicated by: David Preiss
Copyright of article: Copyright 2002, American Mathematical Society

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2008, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google