Phillips-Type Theorems for Nikol'skii and Certain Other Function Spaces

Analogues of the Phillips theorem are obtained for anisotropic Nikol'skii, Besov, and Lizorkin–Triebel spaces of functions defined on irregular domains (in particular, on open sets), as well as for the spaces, closely related to the above spaces, that are defined by local best approximations by polynomials in different metrics (including the spaces of DeVore and Sharpley and BMO).