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

Morbidelli, Daniele

Studia Mathematica, Tome 141 (2000), p. 213-244 / Harvested from The Polish Digital Mathematics Library

Résumé

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.

Détail

Publié le : 2000-01-01

Zbl 0981.46034

EUDML-ID : urn:eudml:doc:216720

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