Sobolev-type integral representations for functions defined on Carnot groups

E. A. Plotnikova

Matematičeskie trudy, Tome 11 (2008) no. 1, pp. 113-131.

Résumé

We obtain some integral representations of the form $f(x)=P(f)+K(\nabla f)$ on the Carnot groups, where $P(f)$ is a polynomial and $K$ is an integral operator with a specific singularity. These representations are employed to prove the weak Poincaré inequality.

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