On Approximation Orders of Functions of Several Variables in the Lorentz Space

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 establ...

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Veröffentlicht in:	Proceedings of the Steklov Institute of Mathematics 2018-04, Vol.300 (Suppl 1), p.9-24
1. Verfasser:	Akishev, G.
Format:	Artikel
Sprache:	eng
Schlagworte:	Anisotropy Approximation Mathematical analysis Mathematics Mathematics and Statistics Periodic functions
Online-Zugang:	Volltext
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Zusammenfassung:	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.
ISSN:	0081-5438 1531-8605
DOI:	10.1134/S0081543818020037