Extension of Lipschitz Functions Defined on Metric Subspaces of Homogeneous Type

Details Extension of Lipschitz Functions Defined on Metric Subspaces of Homogeneous Type Extension of Lipschitz Functions Defined on Metric Subspaces of Homogeneous Type

2006-09-19

arxiv.org/abs/math/0609535v1

Rev. Mat. Complut., 19 (2006), no. 2, 347-359

Mathematics

Functional Analysis

12 pages

Scientific paper

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 $\mu$.

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