Spaces of Functions of Fractional Smoothness on an Irregular Domain

In this paper, we study the spaces $B_{pq}^s (G)$ and $L_{pq}^s (G)$ of functions with positive exponent of smoothness $s > 0$, defined on a domain $G\subset\mathbb R^n$. For a domain $G$ with specific geometric properties, we establish the embedding $B_{pp}^s(G)=L_{pp}^s(G)\subset L_q(G)$, $1<p<q<\infty$, with the relationship between the parameters defined by these geometric properties.