Local approximations of differentiable functions
In this paper the author provides descriptions of some spaces of differentiable functions constructed from \(L_p\) spaces, \(0< p <\infty\). These descriptions are given in terms of local and piecewise polynomial approximations (cf. Theorems 3, 4, 5 and 6). The results of the author are mainly based on the reduction of the assumptions from a Bernstein theorem into the uniform convergence of certain sequence of functions.
local and piecewise polynomial approximations
scientific article; zbMATH DE number 6682154