Linear and nonlinear extensions of Lipschitz functions from subsets of metric spaces
HTML articles powered by AMS MathViewer
- by A. Brudnyi and Y. Brudnyi
- St. Petersburg Math. J. 19 (2008), 397-406
- DOI: https://doi.org/10.1090/S1061-0022-08-01003-0
- Published electronically: March 21, 2008
- PDF | Request permission
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
- A. Brudnyĭ and Yu. Brudnyĭ, Simultaneous extensions of Lipschitz functions, Uspekhi Mat. Nauk 60 (2005), no. 6(366), 53–72 (Russian, with Russian summary); English transl., Russian Math. Surveys 60 (2005), no. 6, 1057–1076. MR 2215754, DOI 10.1070/RM2005v060n06ABEH004281
- Alexander Brudnyi and Yuri Brudnyi, Metric spaces with linear extensions preserving Lipschitz condition, Amer. J. Math. 129 (2007), no. 1, 217–314. MR 2288741, DOI 10.1353/ajm.2007.0000
- Martin R. Bridson and André Haefliger, Metric spaces of non-positive curvature, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 319, Springer-Verlag, Berlin, 1999. MR 1744486, DOI 10.1007/978-3-662-12494-9
- Aryeh Dvoretzky, Some results on convex bodies and Banach spaces, Proc. Internat. Sympos. Linear Spaces (Jerusalem, 1960) Jerusalem Academic Press, Jerusalem; Pergamon, Oxford, 1961, pp. 123–160. MR 0139079
- William B. Johnson, Joram Lindenstrauss, and Gideon Schechtman, Extensions of Lipschitz maps into Banach spaces, Israel J. Math. 54 (1986), no. 2, 129–138. MR 852474, DOI 10.1007/BF02764938
- N. J. Kalton, Spaces of Lipschitz and Hölder functions and their applications, Collect. Math. 55 (2004), no. 2, 171–217. MR 2068975
- James R. Lee and Assaf Naor, Extending Lipschitz functions via random metric partitions, Invent. Math. 160 (2005), no. 1, 59–95. MR 2129708, DOI 10.1007/s00222-004-0400-5
- Hassler Whitney, Analytic extensions of differentiable functions defined in closed sets, Trans. Amer. Math. Soc. 36 (1934), no. 1, 63–89. MR 1501735, DOI 10.1090/S0002-9947-1934-1501735-3
Bibliographic Information
- A. Brudnyi
- Affiliation: Department of Mathematics and Statistics, University of Calgary, Calgary, Canada
- MR Author ID: 292684
- Email: albru@math.ucalgary.ca
- Y. Brudnyi
- Affiliation: Department of Mathematics, Technion, Haifa, Israel
- Email: ybrudnyi@math.technion.ac.il
- Received by editor(s): April 20, 2006
- Published electronically: March 21, 2008
- Additional Notes: Supported in part by NSERC
- © Copyright 2008 American Mathematical Society
- Journal: St. Petersburg Math. J. 19 (2008), 397-406
- MSC (2000): Primary 54E40
- DOI: https://doi.org/10.1090/S1061-0022-08-01003-0
- MathSciNet review: 2340707