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Extensions of lipschitz maps into Banach spaces

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Abstract

It is proved that ifY ⊂X are metric spaces withY havingn≧2 points then any mapf fromY into a Banach spaceZ can be extended to a map\(\hat f\) fromX intoZ so that\(\left\| {\hat f} \right\|_{lip} \leqq c log n\left\| f \right\|_{lip} \) wherec is an absolute constant. A related result is obtained for the case whereX is assumed to be a finite-dimensional normed space andY is an arbitrary subset ofX.

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Authors and Affiliations

  1. Ohio State University, 43210, Columbus, OH, USA

    William B. Johnson, Joram Lindenstrauss & Gideon Schechtman

  2. Texas A&M University, College Station, Texas, USA

    William B. Johnson

  3. The Hebrew University of Jerusalem, Jerusalem, Israel

    Joram Lindenstrauss

  4. The Weizmann Institute of Science, 76100, Rehovot, Israel

    Gideon Schechtman

Authors
  1. William B. Johnson
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  2. Joram Lindenstrauss
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  3. Gideon Schechtman
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Additional information

Supported in part by US-Israel Binational Science Foundation and by NSF MCS-7903042.

Supported in part by NSF MCS-8102714.

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Johnson, W.B., Lindenstrauss, J. & Schechtman, G. Extensions of lipschitz maps into Banach spaces. Israel J. Math. 54, 129–138 (1986). https://doi.org/10.1007/BF02764938

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  • DOI: https://doi.org/10.1007/BF02764938

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