Sobolev's embedding theorem for a domain with irregular boundary

In Sobolev's embedding theorem, $W_p^s(G)\subset L_q(G)$ the relations between admissible smoothness parameters and integrability parameters are determined by the geometric properties of the domain $G$. In the present paper this result and the corresponding estimates of weak type are established for domains with irregular boundaries and in the case of weighted $L_p$, $L_q$-spaces.