# Extension of Lipschitz functions defined on metric subspaces of homogeneous type.

Alexander Brudnyi; Yuri Brudnyi

Revista Matemática Complutense (2006)

- Volume: 19, Issue: 2, page 347-359
- ISSN: 1139-1138

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topBrudnyi, Alexander, and Brudnyi, Yuri. "Extension of Lipschitz functions defined on metric subspaces of homogeneous type.." Revista Matemática Complutense 19.2 (2006): 347-359. <http://eudml.org/doc/41906>.

@article{Brudnyi2006,

abstract = {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.},

author = {Brudnyi, Alexander, Brudnyi, Yuri},

journal = {Revista Matemática Complutense},

keywords = {Funciones de varias variables; Función lipschitziana; Espacios métricos; metric space; doubling measure; linear extension},

language = {eng},

number = {2},

pages = {347-359},

title = {Extension of Lipschitz functions defined on metric subspaces of homogeneous type.},

url = {http://eudml.org/doc/41906},

volume = {19},

year = {2006},

}

TY - JOUR

AU - Brudnyi, Alexander

AU - Brudnyi, Yuri

TI - Extension of Lipschitz functions defined on metric subspaces of homogeneous type.

JO - Revista Matemática Complutense

PY - 2006

VL - 19

IS - 2

SP - 347

EP - 359

AB - 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.

LA - eng

KW - Funciones de varias variables; Función lipschitziana; Espacios métricos; metric space; doubling measure; linear extension

UR - http://eudml.org/doc/41906

ER -

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