TY - JOUR
T1 - Spectral calculus and lipschitz extension for barycentric metric spaces dedicated to nigel kalton
AU - Mendel, Manor
AU - Naor, Assaf
N1 - Publisher Copyright:
© Versita sp. z o.o.
PY - 2013
Y1 - 2013
N2 - The metric Markov cotype of barycentric metric spaces is computed, yielding the first class of metric spaces that are not Banach spaces for which this bi-Lipschitz invariant is understood. It is shown that this leads to new nonlinear spectral calculus inequalities, as well as a unified framework for Lipschitz extension, including new Lipschitz extension results for CAT (0) targets. An example that elucidates the relation between metric Markov cotype and Rademacher cotype is analyzed, showing that a classical Lipschitz extension theorem of Johnson, Lindenstrauss and Benyamini is asymptotically sharp.
AB - The metric Markov cotype of barycentric metric spaces is computed, yielding the first class of metric spaces that are not Banach spaces for which this bi-Lipschitz invariant is understood. It is shown that this leads to new nonlinear spectral calculus inequalities, as well as a unified framework for Lipschitz extension, including new Lipschitz extension results for CAT (0) targets. An example that elucidates the relation between metric Markov cotype and Rademacher cotype is analyzed, showing that a classical Lipschitz extension theorem of Johnson, Lindenstrauss and Benyamini is asymptotically sharp.
KW - Cat (0) metric spaces
KW - Lipschitz extension
KW - Markov cotype
KW - Nonlinear spectral gaps
UR - http://www.scopus.com/inward/record.url?scp=85017320580&partnerID=8YFLogxK
U2 - 10.2478/agms-2013-0003
DO - 10.2478/agms-2013-0003
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:85017320580
SN - 2299-3274
VL - 1
SP - 163
EP - 199
JO - Analysis and Geometry in Metric Spaces
JF - Analysis and Geometry in Metric Spaces
IS - 1
ER -