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.