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Estimates of the asymptotic characteristics of classes of functions with bounded mixed derivative or difference. (English. Russian original) Zbl 0719.46021
Proc. Steklov Inst. Math. 189, 161-197 (1990); translation from Tr. Mat. Inst. Steklova 189, 138-168 (1989).
[For the entire collection see Zbl 0666.00008.]
The author establishes the orders of the \(\epsilon\)-entropy, Kolmogorov’s diameters, orthodiameters of the classes \(W^ F_{q,\alpha}\), \(H^ F_ q\) in the spaces \(L_ p\) for some connections between p and q.

MSC:
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
46E39 Sobolev (and similar kinds of) spaces of functions of discrete variables
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
41A46 Approximation by arbitrary nonlinear expressions; widths and entropy