Displaying similar documents to “Some relations among volume, intrinsic perimeter and one-dimensional restrictions of B V functions in Carnot groups”

Homogeneous Carnot groups related to sets of vector fields

Andrea Bonfiglioli (2004)

Bollettino dell'Unione Matematica Italiana

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In this paper, we are concerned with the following problem: given a set of smooth vector fields X 1 , … , X m on R N , we ask whether there exists a homogeneous Carnot group G = ( R N , ∘ , δ λ ) such that ∑ i X i 2 is a sub-Laplacian on G . We find necessary and sufficient conditions on the given vector fields in order to give a positive answer to the question. Moreover, we explicitly construct the group law i as above, providing direct proofs. Our main tool is a suitable version of the Campbell-Hausdorff formula. Finally, we...

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.

Sobolev spaces of integer order on compact homogeneous manifolds and invariant differential operators

Cristiana Bondioli (1996)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Let M be a Riemannian manifold, which possesses a transitive Lie group G of isometries. We suppose that G , and therefore M , are compact and connected. We characterize the Sobolev spaces W p 1 ⁢ M 1 < p < + ∞ by means of the action of G on M . This characterization allows us to prove a regularity result for the solution of a second order differential equation on M by global techniques.

Function spaces of Nikolskii type on compact manifold

Cristiana Bondioli (1992)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Nikolskii spaces were defined by way of translations on R n and by way of coordinate maps on a differentiable manifold. In this paper we prove that, for functions with compact support in R n , we get an equivalent definition if we replace translations by all isometries of R n . This result seems to justify a definition of Nikolskii type function spaces on riemannian manifolds by means of a transitive group of isometries (provided that one exists). By approximation theorems, we prove that - for...