Full paper in PDF:
$% A. Brudnyi and Yu. Brudnyi, Extension of Lipschitz functions defined on metric subspaces of
homogeneous type, Rev. Mat. Complut. 19 (2006), no. 2, 347–359.%$
Department of Mathematics and Statistics University of Calgary Calgary — Canada | |
ABSTRACT
If a metric subspace
of an arbitrary metric space
carries a doubling
measure
, then there is a simultaneous linear extension of all Lipschitz
functions on
ranged in a Banach space to those on
. Moreover, the
norm of this linear operator is controlled by logarithm of the
doubling constant
of
.
Key words: metric space of homogeneous type, Lipschitz function, linear
extension.
2000 Mathematics Subject Classication: primary 26B35; secondary 54E35, 46B15.