Abstract
A new class of rest bounded second variation sequences is introduced. Leindler’s result [7] for such wider class of sequences is proved.
Similar content being viewed by others
References
R. P. Boas, Jr., Integrability Theorems for Trigonometric Transforms, Springer (Berlin-Heidelberg, 1967).
G. H. Hardy, J. E. Littlewood and G. Pólya, Inequalities, University Press (Cambridge, 1934).
A. A. Konyushkov, Best approximation by transforming the Fourier coefficients by the method of arithmetic means and on Fourier series with nonnegative coefficients, Sibirsk. Mat. J., 3 (1962), 56–78 (in Russian).
L. Leindler, Further sharpening of inequalities of Hardy and Littlewood, Acta Sci. Math. (Szeged), 54 (1990), 285–289.
L. Leindler, Embedding results pertaining to strong approximation of Fourier series. II, Analysis Math., 23 (1997), 223–240.
L. Leindler, A new class of numerical sequences and its applications to sine and cosine series, Analysis Math., 28 (2002), 279–286.
L. Leindler, A theorem on Besov-Nikol’skiĭ class, Publ. Math. Debrecen, 64 (2004), 237–248.
L. Leindler, A note on the best approximation of sine and cosine series, Analysis Math., 32 (2006), 155–161.
M. K. Potapov and M. Berisha, Moduli of smoothness and Fourier coefficients of periodic functions of one variable, Publ. de l’institut Math., 26 (1979), 215–228.
M. K. Potapov and B. V. Somonov, On the interrelation of the generalized Besov-Nikol’skiĭ and Weyl-Nikol’skiĭ classes of functions, Analysis Math., 22 (1996), 299–316
M. Riesz, Sur les fonctions conjuguées, Math. Z., 27 (1927), 218–244.
S. Yu. Tikhonov, Fourier coefficients of functions from Besov-Nikol’skiĭ class, Vestn. MGU, Ser. 1. Mat.-Mech., 6 (2002), 26–35 (in Russian).
S. Yu. Tikhonov, Characteristics of Besov-Nikol’skiĭ class of functions, Electronic Transactions on Numerical Analysis, 19 (2005), 94–104.
M. F. Timan, Peculiarities of Fundamental Theorems of the Constructive Theory of Functions in the Spaces L p, Studies on Contemporary Problems in Constructive Theory of Functions, Izdat. Akad. Nauk Az. SSSR (Baku, 1965).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Szal, B. Generalization of a theorem on Besov-Nikol’skiĭ classes. Acta Math Hung 125, 161–181 (2009). https://doi.org/10.1007/s10474-009-8252-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10474-009-8252-5