Extension of Lipschitz Functions Defined on Metric Subspaces of Homogeneous Type

Abstract

If a metric subspace $M^o$ of an arbitrary metric space $M$ carries a doubling measure $\mu$, then there is a simultaneous linear extension of all Lipschitz functions on $M^o$ 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 $\mu$.

12 pages