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The ortho-diameters of Nikol’skii and Besov classes in the Lorentz spaces. (English. Russian original) Zbl 1189.46019
Russ. Math. 53, No. 2, 21-29 (2009); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2009, No. 2, 25-33 (2009).
V. N. Temlyakov has introduced the notion of the ortho-diameter of functional classes and he has obtained estimates for ortho-diameters of Sobolev and Nikol’skii classes in Lebesgue spaces [Sov. Phys. Dokl. 267, 314–317 (1982; Zbl 0524.41013); “Approximation of functions with bounded mixed derivative” (Trudy Matematicheskogo Instituta im. V. A. Steklova 178; Moskva: “Nauka”) (1986; Zbl 0625.41028)]. This research has been developed in [D. Zung, Math. USSR, Sb. 59, 247–267 (1988); translation from Mat. Sb., Nov. Ser. 131(173), No. 2(10), 251–271 (1986; Zbl 0634.42005)], E. M. Galeev [Math. Notes 43, No. 2, 110–118 (1988); translation from Mat. Zametki 43, No. 2, 197–211 (1988; Zbl 0659.42008)] and N. N. Pustovoitov [Izv. Math. 64, No. 1, 121–141 (2000); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 64, No. 1, 123–144 (2000; Zbl 1007.42004)]. The aim of the paper under review is to estimate the ortho-diameters of Nikol’skij and Besov classes in norms of anisotropic Lorentz spaces.

MSC:
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
41A30 Approximation by other special function classes
41A46 Approximation by arbitrary nonlinear expressions; widths and entropy
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References:
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