Extension of Lipschitz Functions Defined on Metric Subspaces of Homogeneous Type - Brudnyi, Alexander; Brudnyi, Yuri (Revista Matemática Complutense, 2006)
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.