Abstract:
We consider the anisotropic Lorentz space of periodic functions. Sufficient conditions are proved for a function to belong to the anisotropic Lorentz space. Estimates for the order of approximation by trigonometric polynomials of the Nikol'skii-Besov class in the anisotropic Lorentz space are established.
Keywords:
Lorentz space, Nikol'skii-Besov class, best approximation.
Citation:
G. A. Akishev, “On approximation orders of functions of several variables in the Lorentz space”, Trudy Inst. Mat. i Mekh. UrO RAN, 22, no. 4, 2016, 13–28; Proc. Steklov Inst. Math. (Suppl.), 300, suppl. 1 (2018), 9–24
\Bibitem{Aki16}
\by G.~A.~Akishev
\paper On approximation orders of functions of several variables in the Lorentz space
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2016
\vol 22
\issue 4
\pages 13--28
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\crossref{https://doi.org/10.21538/0134-4889-2016-22-4-13-28}
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\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2018
\vol 300
\issue , suppl. 1
\pages 9--24
\crossref{https://doi.org/10.1134/S0081543818020037}
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Linking options:
https://www.mathnet.ru/eng/timm1350
https://www.mathnet.ru/eng/timm/v22/i4/p13
This publication is cited in the following 2 articles:
G. Akishev, “On a function space with mixed generalized logarithmic smoothness”, jour, 2:2 (2024), 4
G. A. Akishev, “O poryadkakh n-chlennykh priblizhenii funktsii mnogikh peremennykh v prostranstve Lorentsa”, Materialy Voronezhskoi mezhdunarodnoi zimnei matematicheskoi shkoly «Sovremennye metody teorii funktsii i smezhnye problemy», Voronezh, 27 yanvarya — 1 fevralya 2023 g. Chast 1, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 227, VINITI RAN, M., 2023, 3–19
Citation in format AMSBIB
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