Volume 19, pp. 94-104, 2005.

Characteristics of Besov-Nikol'skiĭ class of functions

Sergey Tikhonov

Abstract

In this paper we consider functions from a Besov-Nikol'skiǐ, class. We give constructive characteristics of this class. We establish criteria for a function to be in this Besov-Nikol'skiǐ, class by means of conditions on its Fourier coefficients. We also discuss embedding theorems between some classes of functions.

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Key words

Moduli of smoothness, Besov-Nikol'skiǐ, class, Best approximation, Fourier coefficients, Embedding theorems.

AMS subject classifications

42A10, 42A16, 41A50, 42A32, 42A50.

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