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

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.