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Extension of Lipschitz Functions Defined on Metric Subspaces of Homogeneous Type

A. Brudnyi·Yu. Brudnyi
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Abstract

If a metric subspace $M^{o}$ of an arbitrary metric space $M$ carries a doubling measure $μ$, 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 $μ$.

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BibTeXRIS

A. Brudnyi, Yu. Brudnyi. 2006-09-19. Extension of Lipschitz Functions Defined on Metric Subspaces of Homogeneous Type. https://arxiv.org/abs/math/0609535

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