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Laplacians on a family of quadratic Julia sets II
January 2013, 12(1): 59-88. doi: 10.3934/cpaa.2013.12.59
Whitney-type extensions in quasi-metric spaces
Ryan Alvarado 1, , Irina Mitrea 2, and Marius Mitrea 3,
Department of Mathematics, University of Missouri at Columbia, Columbia, MO 65211, United States
Department of Mathematics, Temple University, Philadelphia, PA 19122, United States
Department of Mathematics, University of Missouri, Columbia, MO 65211
Received May 2011 Revised March 2012 Published September 2012
We discuss geometrical scenarios guaranteeing that functions defined on a given set may be extended to the entire ambient, with preservation of the class of regularity. This extends to arbitrary quasi-metric spaces work done by E.J. McShane in the context of metric spaces, and to geometrically doubling quasi-metric spaces work done by H. Whitney in the Euclidean setting. These generalizations are quantitatively sharp.
Keywords: quantitative Urysohn lemma, extension of Hölder functions, extension of Lipschitz functions, Whitney decomposition., geometrically doubling quasi-metric space, partition of unity, quasi-metric space, Hölder functions, metrization, Quasi-metric space, Lipschitz functions, Whitney extension.
Mathematics Subject Classification: Primary: 26A16, 26B35; Secondary 26B05, 54E3.
Citation: Ryan Alvarado, Irina Mitrea, Marius Mitrea. Whitney-type extensions in quasi-metric spaces. Communications on Pure & Applied Analysis, 2013, 12 (1) : 59-88. doi: 10.3934/cpaa.2013.12.59
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Ryan Alvarado Irina Mitrea Marius Mitrea