On the uniform convergence of Walsh-Fourier series (Q1603250)

The generalized Wiener class BV\((p(n) \uparrow p)\) was introduced by \textit{H. Kita} and \textit{K. Yoneda} [Acta Math. Hung. 56, No. 3/4, 229-238 (1990; Zbl 0746.26007)]. In the present paper, the author finds necessary and sufficient conditions in terms of the modulus of continuity \(\omega\) which provide that for any function of the class \(H^{\omega} \bigcap \text{BV}(p(n) \uparrow \infty)\) the Walsh-Fourier series of the function converges to it uniformly on \([0,1]\).