If a metric subspace Mº of an arbitrary metric space M carries a doubling measure μ, then there is a simultaneous linear extension of all Lipschitz functions on Mº ranged in a Banach space to those on M. Moreover, the norm of this linear operator is controlled by logarithm of the doubling constant of μ.
@article{urn:eudml:doc:41906,
title = {Extension of Lipschitz functions defined on metric subspaces of homogeneous type.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {19},
year = {2006},
pages = {347-359},
zbl = {1122.26012},
mrnumber = {MR2241435},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41906}
}
Brudnyi, Alexander; Brudnyi, Yuri. Extension of Lipschitz functions defined on metric subspaces of homogeneous type.. Revista Matemática de la Universidad Complutense de Madrid, Tome 19 (2006) pp. 347-359. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41906/