A Note On Double Walsh$-$Fourier Coefficients of Functions of Generalized Wiener Class

Year 2019, Volume: 7 Issue: 2, 288 - 291, 15.10.2019

Kiran Darji Rajendra Vyas

Abstract

In this note, we have estimated the order of magnitude of double Walsh$-$Fourier coefficients of functions of the class $(\Lambda^1,\Lambda^2)BV (p(n)\uparrow \infty,\varphi, [0,1]^{2})$.

Keywords

double Walsh$-$Fourier coefficients, functions of the class $(\Lambda^1, \Lambda^2)BV (p(n)\uparrow \infty, \varphi, [0, 1

References

• [1] T. Akhobadze, Functions of generalized Wiener classes $BV(p(n)\uparrow \infty, \varphi)$ and their Fourier coefficients, Georgian Math. J., 7 (3) (2000), 401-416.
• [2] K. N. Darji and R. G. Vyas, A note on Walsh-Fourier coefficients, Bull. Math. Anal. Appl., 4 (2) (2012), 116-119.
• [3] K. N. Darji and R. G. Vyas, On absolute convergence of double Walsh-Fourier series, Indian J. Math., 60 (1) (2018), 45-63.
• [4] F. Moricz and A. Veres, Absolute convergence of double Walsh-Fourier series and related results, Acta Math. Hungar., 131(1-2) (2011), 122􀀀137.
• [5] R. G. Vyas, A note on functions of $p(n)-\Lambda-$bounded variation, J. Indian Math. Soc., 78 (1-4) (2011), 215-220.
• [6] R. G. Vyas, On multiple Fourier coefficients of a function of generalized Wiener class, Georgian Math. J., 22 (3) (2015), 435-439.