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Zeitschrift für Analysis und ihre Anwendungen


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Volume 21, Issue 1, 2002, pp. 135–157
DOI: 10.4171/ZAA/1068

Published online: 2002-03-31

Sobolev and Morrey Estimates for Non-Smooth Vector Fields of Step Two

A. Montanari[1] and Daniele Morbidelli[2]

(1) Università di Bologna, Italy
(2) Università di Bologna, Italy

We prove Sobolev-type and Morrey-type inequalities for Sobolev spaces related to a family of non-smooth vector fields which formally satisfy the Hörmander condition of step 2. The coefficients of the vector fields are not regular enough to define the Carnot-Carathéodory distance. Thus the result is proved by developing a real analysis technique which is based on an approximation procedure of Lipschitz continuous vector fields with a family of left-invariant first order operators on a nilpotent Lie group.

Keywords: Sobolev inequalities, Freezing method, homogeneous spaces

Montanari A., Morbidelli Daniele: Sobolev and Morrey Estimates for Non-Smooth Vector Fields of Step Two. Z. Anal. Anwend. 21 (2002), 135-157. doi: 10.4171/ZAA/1068