Spaces of Functions of Fractional Smoothness on an Irregular Domain.

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