Generalized Absolute Convergence of Double Walsh-Fourier Series
DOI:
https://doi.org/10.18311/jims/2024/32951Keywords:
Absolute Convergence, Double Walsh-Fourier Series, Functions of (ϕ, ψ)-(Λ1, Λ2)-Bounded Variation.Abstract
In this paper, we obtain a sufficient condition for the generalized absolute convergence of the double Walsh-Fourier series of a function f of (ϕ, ψ)-(Λ1 , Λ2)-bounded variation.
Downloads
Metrics
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 K. N. Darji, Rajendra Vyas
![Creative Commons License](http://i.creativecommons.org/l/by/4.0/88x31.png)
This work is licensed under a Creative Commons Attribution 4.0 International License.
Accepted 2023-08-29
Published 2024-07-01
References
A. N. Bakhvalov, Fourier coefficients of functions from many-dimensional classes of bounded Λ-variation, Moscow Univ. Math. Bulletin, 66 (1) (2011), 8-16.
K. N. Darji and R. G. Vyas, On absolute convergence of double Walsh−Fourier series, Indian J. Math., 60 (1) (2018), 45-63.
K. N. Darji and R. G. Vyas, On weighted absolute convergence of multiple Fourier series of a function of (p1, ..., pN ) − (Λ1, ..., ΛN)−BV, Acta Math. Hungar., 156 (2) (2018), 361-371.
K. N. Darji and R. G. Vyas, On weighted β-absolute convergence of double Fourier series, J. Classical Anal., 18 (1) (2021), 1-16.
K. N. Darji and R. G. Vyas, Weighted β-absolute convergence of single and double Walsh-Fourier series of functions of ϕ − V −BV , J. Indian Math. Soc., 86 (1-2) (2019), 22-37.
L. Gogoladze and R. Meskhia, On the absolute convergence of trigonometric Fourier series, Proc. Razmadze. Math. Inst., 141 (2006), 29-40.
B. Golubov, A. Efimov and V. Skvortsov, Walsh Series and Transforms: Theory and Applications, Springer Science+Business Media Dordrecht, 1991.
F. M´oricz and A. Veres, On the absolute convergence of multiple Fourier series, Acta Math. Hungar., 117 (3) (2007), 275-292.
M. Schramm and D. Waterman, Absolute convergence of Fourier series of functions of class ΛBV(p) and φΛBV , Acta. Math. Acad. Sci. Hungar., 40 (3-4) (1982), 273-276.
R. G. Vyas, On the absolute convergence of Fourier series of functions of ΛBV(p) and φΛBV , Georgian Math. J., 14 (4) (2007), 769-774.
R. G. Vyas and K. N. Darji, On multiple Fourier coefficients of functions of ϕ − Λ−bounded variation, Math. Inequal. Appl., 17 (3) (2014), 1153-1160.
R. G. Vyas and K. N. Darji, Order of magnitude of multiple Fourier coefficients, Anal. Theory Appl., 29 (1) (2013), 27-36.
A. Zygmund, Trigonometric Series, Vol. I and II. Cambridge University Press, 2nd edn. Reprint, 1979.