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

Boris V. Trushin

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, approximations, and differential equations, Tome 243 (2003), pp. 334-345

Résumé

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.