G. A. Akishev, “On approximation orders of functions of several variables in the Lorentz space”, Trudy Inst. Mat. i Mekh. UrO RAN, 2016, Volume 22, Number 4,Pages <nobr>13

This article is cited in 3 papers

On approximation orders of functions of several variables in the Lorentz space

G. A. Akishev^ab

^a E. A. Buketov Karaganda State University
^b Institute of Mathematics and Computer Science, Ural Federal University, Ekaterinburg

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.

UDC: 517.5

MSC: 41A10, 41A25, 42A10, 46E30, 46E35

Received: 02.09.2016

DOI: 10.21538/0134-4889-2016-22-4-13-28