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March, 2001 Differentiable Control Metrics and Scaled Bump Functions
Alexander Nagel, Elias M. Stein
J. Differential Geom. 57(3): 465-492 (March, 2001). DOI: 10.4310/jdg/1090348130


We show that for each control metric (i.e., Carnot-Caratheodory metric), there is an equivalent metric which has the maximal expected degree of smoothness. The equivalent metric satisfies the natural differential inequalities with respect to the vector fields used to define the metric. This generalizes the regularity of the usual Euclidean metric in Rn. There are also corresponding differential inequalities for scaled "bump functions" supported on balls associated to these metrics. The smooth metrics and bump functions are particularly useful in problems of harmonic analysis in situations where the given metrics arise.


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Alexander Nagel. Elias M. Stein. "Differentiable Control Metrics and Scaled Bump Functions." J. Differential Geom. 57 (3) 465 - 492, March, 2001.


Published: March, 2001
First available in Project Euclid: 20 July 2004

zbMATH: 1041.58006
MathSciNet: MR1882665
Digital Object Identifier: 10.4310/jdg/1090348130

Rights: Copyright © 2001 Lehigh University

Vol.57 • No. 3 • March, 2001
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