ON ESTIMATES FOR ORDERS OF BEST M-TERM APPROXIMATIONS OF MULTIVARIATE FUNCTIONS IN ANISOTROPIC LORENTZ-KARAMATA SPACES
Akishev G.A.
2023Institute of Mathematics with Computing Centre
Ufa Mathematical Journal
2023#15Issue 11 - 20 pp.
In the paper we consider a well-known class of weakly varying functions and by these functions we define an anisotropic Lorentz-Karamata space of 2π-periodic func-tions of many variables. Particular cases of these spaces are anisotropic Lorentz-Zygmund and Lorentz spaces. In the anisotropic Lorentz-Karamata space we define an analogue of Nikolskii-Besov space. The main aim of the paper is to find sharp orders of best M-term trigonometric approximation of functions from Nikolskii-Besov space by the norm of an-other anisotropic Lorentz-Karamata space. In the paper we establish order sharp two-sided estimates of best M-term trigonometric approximations for the functions from the Nikolskii-Besov space in the anisotropic Lorentz-Karamata space in various metrics. In order to prove an upper bound for M-term approximations, we employ an idea of the greedy algorithms proposed by V.N. Temlyakov and we modify it for the anisotropic Lorentz-Karamata space.
Lorentz-Karamata space , M-term approximation , Nikolskii-Besov space
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Kazakhstan branch of Lomonosov Moscow State University, Kazhymukan str. 11, Astana, 100008, Kazakhstan
Institute of Mathematics and Mathematical Modelling, Pushkin str. 125, Almaty, 050010, Kazakhstan
Kazakhstan branch of Lomonosov Moscow State University
Institute of Mathematics and Mathematical Modelling
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