Generalization of a theorem on Besov-Nikol'skiĭ classes
type: Item
instance of: scholarly article
title: Generalization of a theorem on Besov-Nikol'skiĭ classes
zbMATH Open document ID: 1224.26013
author: B. Szal
published in: Acta Mathematica Hungarica
publication date: 2011-02-08T00:00:00Z
review text: The author introduces a class of sequences, the so-called class of rest bounded second variation sequences. He proves that this space is wider than the known classes of quasi-monotone sequences and of rest bounded variation sequences. Known criteria, in terms of the sequence of the Fourier coefficients to be in such classes along with some other conditions for belonging of a function from \(L^p,\) \(1<p<\infty,\) to the Besov-Nikol'skiĭ class are extended to the above new space of sequences. The author starts from results due to Leindler and due to Tikhonov. However, one more paper by \textit{S. Tikhonov} should be added: [J. Math. Anal. Appl. 326, No.~1, 721--735 (2007; Zbl 1106.42003)]; further extensions of sequence classes are given in it which are applicable to the considered problem and related ones.
reviewed by: Elijah Liflyand
Mathematics Subject Classification ID: 26A15
Mathematics Subject Classification ID: 42A16
zbMATH DE Number: 5848554
zbMATH Keywords: Besov-Nikol'skiĭ class
zbMATH Keywords: Fourier coefficient
MaRDI profile type: Publication
full work available at URL: s10474-009-8252-5
OpenAlex ID: W1993851268
cites work: Q5521650
cites work: Q3348233
cites work: Embedding results pertaining to strong approximation of Fourier series. II
cites work: A new class of numerical sequences and its applications to sine and cosine series
cites work: Q4816492
cites work: A note on the best approximation of sine and cosine series
cites work: On the interrelation of the generalized Besov-Nikols'kiǐ and Weyl-Nikols'kiǐ classes of functions
cites work: Characteristics of Besov-Nikol'skiĭ class of functions
DOI: 10.1007/S10474-009-8252-5
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description: scientific article; zbMATH DE number 5848554