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Linear and nonlinear extensions of Lipschitz functions from subsets of metric spaces
Author(s):
A.
Brudnyi;
Y.
Brudnyi
Original publication:
Algebra i Analiz,
tom 19
(2007),
nomer 3.
Journal:
St. Petersburg Math. J.
19
(2008),
397-406.
MSC (2000):
Primary 54E40
Posted:
March 21, 2008
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Abstract:
A relationship is established between the linear and nonlinear extension constants for Lipschitz functions defined on subsets of metric spaces. Proofs of several results announced in our earlier paper are presented.
References:
-
- [BB1]
- A. Brudnyı and Yu. Brudnyı, Simultaneous extensions of Lipschitz functions, Uspekhi Mat. Nauk 60 (2005), no. 6, 53-72; English transl., Russian Math. Surveys 60 (2005), no. 6, 1057-1076. MR 2215754 (2007f:26004)
- [BB2]
- -, Metric spaces with linear extensions preserving Lipschitz condition, Amer. J. Math. 129 (2007), 217-314. MR 2288741
- [BH]
- M. Bridson and A. Haefliger, Metric spaces of non-positive curvature, Grundlehren Math. Wiss., Bd. 319, Springer-Verlag, Berlin, 1999. MR 1744486 (2000k:53038)
- [D]
- A. Dvoretzky, Some results on convex bodies and Banach spaces, Proc. Internat. Sympos. Linear Spaces (Hebrew Univ., Jerusalem, 1960), Jerusalem Acad. Press, Jerusalem, 1961, pp. 123-160. MR 0139079 (25:2518)
- [JLSch]
- W. B. Johnson, J. Lindenstrauss, and G. Schechtman, Extensions of Lipschitz maps into Banach spaces, Israel J. Math. 54 (1986), no. 2, 129-138. MR 0852474 (87k:54021)
- [K]
- N. Kalton, Spaces of Lipschitz and Hölder functions and their applications, Collect. Math. 55 (2004), no. 2, 171-217. MR 2068975 (2005c:46113)
- [LN]
- J. R. Lee and A. Naor, Extending Lipschitz functions via random metric partitions, Invent. Math. 160 (2005), no. 1, 59-95. MR 2129708 (2006c:54013)
- [W]
- H. Whitney, Analytic extensions of differentiable functions defined in closed sets, Trans. Amer. Math. Soc. 36 (1934), 63-89. MR 1501735
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Additional Information:
A.
Brudnyi
Affiliation:
Department of Mathematics and Statistics, University of Calgary, Calgary, Canada
Email:
albru@math.ucalgary.ca
Y.
Brudnyi
Affiliation:
Department of Mathematics, Technion, Haifa, Israel
Email:
ybrudnyi@math.technion.ac.il
DOI:
10.1090/S1061-0022-08-01003-0
PII:
S 1061-0022(08)01003-0
Keywords:
Lipschitz function,
linear extension operator,
Banach space
Received by editor(s):
20/APR/2006
Posted:
March 21, 2008
Additional Notes:
Supported in part by NSERC
Copyright of article:
Copyright
2008,
American Mathematical Society
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