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 . For a domain G with specific geometric properties, we establish the embedding B _pq ^s (G) = L _pq ^s (G) L _q (G), 1 < p < q < , with the relationship between the parameters defined by these geometric properties.