In 1940 R. Salem formulated a
sufficient condition for a continuous and periodic function to have a trigonometric
Fourier series which converges uniformly to the function. In this paper we will
formulate a similar condition, which implies that the Walsh-Fourier series of such a
function has this property. Furthermore we show that our result is stronger than
certain classical results, and that it also implies the uniform convergence of the
Walsh-Fourier series of certain classes of continuous functions of generalized bounded
variation. The latter is analogous to results obtained by L. C. Young and R. Salem
for trigonometric Fourier series.
