Geodesic
Coercive estimates and integral representation formulas on Carnot groups
Eurasian mathematical journal, Tome 1 (2010) no. 3, pp. 58-96

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For general Carnot groups, we obtain coercive estimates for homogeneous differential operators with constant coefficients, kernels of which have finite dimension. We develop new Sobolev-type integral representations of differentiable functions which are a crucial tool for deriving coercive estimates. Moreover we prove some auxiliary results having independent interest, in particular, Sobolev type embedding and compactness theorems for John domains. 
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     author = {D. V. Isangulova and S. K. Vodopyanov},
     title = {Coercive estimates and integral representation formulas on {Carnot} groups},
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D. V. Isangulova; S. K. Vodopyanov. Coercive estimates and integral representation formulas on Carnot groups. Eurasian mathematical journal, Tome 1 (2010) no. 3, pp. 58-96. http://geodesic.mathdoc.fr/item/EMJ_2010_1_3_a4/