The Extension of Functions of Sobolev Classes Beyond the Boundary of the~Domain on Carnot Groups

I. M. Pupyshev

Matematičeskie trudy, Tome 10 (2007) no. 2, pp. 187-212.

Résumé

We prove the theorem on extension of the functions of the Sobolev space $W^l_p(\Omega)$ which are defined on a bounded $(\varepsilon,\delta)$-domain $\Omega$ in a two-step Carnot group beyond the boundary of the domain of definition. This theorem generalizes the well-known extension theorem by P. Jones for domains of the Euclidean space.

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