Abstract
We consider classes of periodic functions of bounded Λ-variation, where Λ has a power growth rate. We show that this class contains a continuous function whose Cesaro means of the Fourier series (whose order depends on the growth rate of Λ) have no localization property.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
D. Waterman, “On Convergence of Fourier Series of Functions of Generalized Bounded Variation,” Studia math. 44(2), 107–117 (1972).
D. Waterman, “On the Summability of Fourier Series of Functions of Λ-Bounded Variation,” Studia math. 55(1), 87–95 (1976).
A. Zygmund, Trigonometric Series (Cambridge University Press, 2nd ed., 1959; Mir, Moscow, 1965, Vol. 1).
A. I. Sablin, “λ-Variation and Fourier Series,” Izv. Vyssh.Uchebn. Zaved. Mat. No. 10, 66–68 (1987) [Soviet Mathematics (Iz. VUZ) 31 (10), 64–66 (1987)].
S. Perlman and D. Waterman, “Some Remarks on Functions of Λ-Bounded Variation,” Proc. Amer. Math. Soc. 74(1), 113–118 (1979).
D. Waterman, “On Λ-Bounded Variation,” Studia math. 57(1), 33–45 (1976).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © A.N. Bakhvalov, 2011, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2011, No. 8, pp. 9–13.
About this article
Cite this article
Bakhvalov, A.N. Localization of Cesaro means of Fourier series for functions of bounded Λ-variation. Russ Math. 55, 7–10 (2011). https://doi.org/10.3103/S1066369X11080020
Received:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S1066369X11080020