Embeddings of spaces of functions with variable smoothness. (Q1377926)

The author studies embeddings of weighted spaces of differentiable functions defined on a domain \(G\subset\mathbb R^ n\) with sufficiently smooth boundary, namely, he establishes embeddings of weighted Sobolev spaces or weighted Besov spaces into a space of the same type. The theorems presented in the paper cover author's previous non-weighted results [see O. V. Besov, V. P. Il'in and S. M. Nikol'skiĭ\, Integral representations of functions and imbedding theorems (Russian)(Moskva, Nauka, Fizmatlit)(1996; Zbl 0867.46026), O. V. Besov, Integral representations of functions and the embedding theorems for a domain with flexible horn condition (Russian), Tr. Mat. Inst. Steklova 170, 12--30(1984; Zbl 0582.46037) and O. V. Besov, Estimates of integral continuity moduli and imbedding theorems for domains with the flexible horn conditions (Russian), Tr. Mat. Inst. Steklova 172, 4--15(1985; Zbl 0587.46032)].