Spaces of Functions of Fractional Smoothness on an Irregular Domain

In this paper, we study the spaces Bpqs(G) and Lpqs(G) of functions with positive exponent of smoothness s > 0, defined on a domain \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\user1{G} \subset \mathbb{R}^\user1{n} $$ \end{document}. For a domain G with specific geometric properties, we establish the embedding Bpqs(G) = Lpqs(G) ⊂ Lq(G), 1 < p < q < ∞, with the relationship between the parameters defined by these geometric properties.