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 Algebra i Analiz: Year: Volume: Issue: Page: Find

 Algebra i Analiz, 2007, Volume 19, Issue 3, Pages 106–118 (Mi aa121)

Research Papers

Linear and nonlinear extensions of Lipschitz functions from subsets of metric spaces

A. Brudnyia, Y. Brudnyib

a Department of Mathematics and Statistics, University of Calgary, Calgary, Canada
b Department of Mathematics, Technion, Haifa, Israel

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.

Keywords: Lipschitz function, linear extension operator, Banach space.

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English version:
St. Petersburg Mathematical Journal, 2008, 19:3, 397–406

Bibliographic databases:

MSC: 54E40
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Citation: A. Brudnyi, Y. Brudnyi, “Linear and nonlinear extensions of Lipschitz functions from subsets of metric spaces”, Algebra i Analiz, 19:3 (2007), 106–118; St. Petersburg Math. J., 19:3 (2008), 397–406

Citation in format AMSBIB
\Bibitem{BruBru07} \by A.~Brudnyi, Y.~Brudnyi \paper Linear and nonlinear extensions of Lipschitz functions from subsets of metric spaces \jour Algebra i Analiz \yr 2007 \vol 19 \issue 3 \pages 106--118 \mathnet{http://mi.mathnet.ru/aa121} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2340707} \zmath{https://zbmath.org/?q=an:1213.54040} \elib{http://elibrary.ru/item.asp?id=9540303} \transl \jour St. Petersburg Math. J. \yr 2008 \vol 19 \issue 3 \pages 397--406 \crossref{https://doi.org/10.1090/S1061-0022-08-01003-0} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000267653300003} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. Naor A., Sheffield S., “Absolutely minimal Lipschitz extension of tree-valued mappings”, Math. Ann., 354:3 (2012), 1049–1078
2. Meyerson W., “Lipschitz and Bilipschitz Maps on Carnot Groups”, Pac. J. Math., 263:1 (2013), 143–170
3. Naor A., “Probabilistic Clustering of High Dimensional Norms”, Proceedings of the Twenty-Eighth Annual Acm-SIAM Symposium on Discrete Algorithms, Assoc Computing Machinery, 2017, 690–709
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