Embedding of the Sobolev Space into the Orlicz and BMO Spaces with Power Weights

In the embedding theorems $W_p^s(G) \subset L_q (G)$, $W_p^s(G)\subset L_{\Phi}(G)$, and $W_p^s(G)\subset\mathrm{BMO}(G)$, admissible relations between the smoothness and summability parameters are determined by the geometric properties of the underlying domain $G$. These theorems are proved here for domains with irregular boundary. The results are extended to weighted spaces.