Extension of Lipschitz functions defined on metric subspaces of homogeneous type

• Autores: Yuri Brudnyi, Alexander Brudnyi
• Localización: Revista matemática complutense, ISSN-e 1988-2807, ISSN 1139-1138, Vol. 19, Nº 2, 2006, págs. 347-359
• Idioma: inglés
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• Resumen

  • 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.