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Title

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

Authors 1

Affiliations

  1. Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato 5, 40127 Bologna, Italy

Abstract

We study the notion of fractional Lp-differentiability of order s∈(0,1) along vector fields satisfying the Hörmander condition on ℝn. 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 Ws,p-norms are equivalent. We also prove a local embedding W1,p⊂Ws,q, where q is a suitable exponent greater than p.

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Studia Mathematica
2000/139/3
Export to PBN, Opens in new tab
Pages:
213-244
Main language of publication
English
Received
1998-11-23
Accepted
2000-01-05
Published
2000
Exact and natural sciences