Extending functions from Nikolskii-Besov spaces of mixed smoothness beyond a cube

Abstract

The article examines Nikolskii and Besov spaces with norms defined using "$L_p$-averaged" mixed moduli of continuity of functions of appropriate orders, instead of mixed moduli of continuity of known orders for certain mixed derivative functions. The author builds continuous linear mappings of such spaces of functions defined on cube $I^d,$ to ordinary Nikolskii and Besov spaces of mixed smoothness in ${\mathbb{R}}^d,$ that are function extension operators, thus incurring coincidence of both kinds of spaces on the cube $I^d.$

russian, 61 pages