The Traces of Bessel Potentials on Regular Subsets of Carnot Groups

We prove the direct theorem on the traces of the Bessel potentials $L^\alpha_p$ defined on a Carnot group, on the regular closed subsets called Ahlfors $d$-sets. The result is convertible for integer $\alpha$, i.e., for the Sobolev spaces $W^\alpha_p$ (the converse trace theorem was proven in [1]). This theorem generalizes A. Johnsson and H. Wallin's results [2] for Sobolev functions and Bessel potentials on the Euclidean space.