Convergence of multiple Fourier-Walsh series of functions of bounded \(\Lambda\)-variation. (English. Russian original) Zbl 1339.42020
J. Contemp. Math. Anal., Armen. Acad. Sci. 40, No. 2, 1-13 (2005); translation from Izv. Nats. Akad. Nauk Armen., Mat. 40, No. 2, 3-14 (2005).
Summary: The article proves that if a summable function \(f(x,y)\) belongs to Waterman’s class \(\Lambda BV([0,1]^2)\) for \(\Lambda=\left\{\overline o\left(\frac{\sqrt n}{\sqrt{\ln(n+1)}}\right)\right\}^\infty_{n=1}\) and is continuous at every point of some compact \(E\), then the double Fourier-Walsh series of \(f(x,y)\) is uniformly \(u(K)\)-convergent on \(E\).
MSC:
| 42C10 | Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) |
