Lipschitz extension of multiple Banach-valued functions in the sense of Almgren

• Autores: Jordan Goblet
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 35, Nº 1, 2009, págs. 223-231
• Idioma: inglés
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• Resumen

  • For any positive integer Q, a Q(Y)-valued function f on X is essentially a rule assigning Q unordered and not necessarily distinct elements of Y to each element of X. Equivalently f maps X into the space Q(Y) of Q unordered points in Y. We study the Lipschitz extension problem in this context by using two general Lipschitz extension theorems recently proved by U. Lang and T. Schlichenmaier. We prove that the pair (X,Q(Y)) has the Lipschitz extension property if Y is a Banach space and X is a metric space with a finite Nagata dimension. We also show that Q(Y) is an absolute Lipschitz retract if Y is a finite algebraic dimensional Banach space.