The ortho-diameters of Nikol'skii and Besov classes in the Lorentz spaces
\textit{V.\,N.\thinspace 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 [\textit{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)], \textit{E.\,M.\thinspace Galeev} [Math.\ Notes 43, No.\,2, 110--118 (1988); translation from Mat.\ Zametki 43, No.\,2, 197--211 (1988; Zbl 0659.42008)] and \textit{N.\,N.\thinspace 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.
scientific article; zbMATH DE number 5621403