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Displaying similar documents to “Homogeneous Carnot groups related to sets of vector fields”

Fractional Sobolev norms and structure of Carnot-Carathéodory balls for Hörmander vector fields

Daniele Morbidelli (2000)

Studia Mathematica

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We study the notion of fractional L p -differentiability of order s ∈ ( 0 , 1 ) along vector fields satisfying the Hörmander condition on ℝ n . We prove a modified version of the celebrated structure theorem for the Carnot-Carathéodory balls originally due to Nagel, Stein and Wainger. This result enables us to demonstrate that different W s , p -norms are equivalent. We also prove a local embedding W 1 , p ⊂ W s , q , where q is a suitable exponent greater than p.

Some relations among volume, intrinsic perimeter and one-dimensional restrictions of B V functions in Carnot groups

Francescopaolo Montefalcone (2005)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Let 𝔾 be a k -step Carnot group. The first aim of this paper is to show an interplay between volume and 𝔾 -perimeter, using one-dimensional horizontal slicing. What we prove is a kind of Fubini theorem for 𝔾 -regular submanifolds of codimension one. We then give some applications of this result: slicing of B V 𝔾 functions, integral geometric formulae for volume and 𝔾 -perimeter and, making use of a suitable notion of convexity, called, we state a Cauchy type formula for 𝔾 -convex sets. Finally,...