Revista Matemática Iberoamericana

Multi-parameter Carnot-Carathéodory balls and the theorem of Frobenius

Brian Street

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We study multi-parameter Carnot-Carathéodory balls, generalizing results due to Nagel, Stein and Wainger in the single parameter setting. The main technical result is seen as a uniform version of the theorem of Frobenius. In addition, we study maximal functions associated to certain multi-parameter families of Carnot-Carathéodory balls.

Article information

Rev. Mat. Iberoamericana, Volume 27, Number 2 (2011), 645-732.

First available in Project Euclid: 10 June 2011

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Zentralblatt MATH identifier

Primary: 53C17: Sub-Riemannian geometry
Secondary: 53C12: Foliations (differential geometric aspects) [See also 57R30, 57R32] 42B25: Maximal functions, Littlewood-Paley theory

sub-Riemannian geometry Carnot-Carathéodory geometry Frobenius theorem multi-parameter spaces of homogeneous type maximal functions


Street, Brian. Multi-parameter Carnot-Carathéodory balls and the theorem of Frobenius. Rev. Mat. Iberoamericana 27 (2011), no. 2, 645--732.

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