On the Strong Summability of Fourier-Walsh Series in the Besov Space

The Fourier-Walsh series of even continuous functions may be divergent at some points. Moreover, among integrable functions, there are functions such that their Fourier-Walsh series diverge everywhere on [0, 1). In this connection, it becomes necessary to consider various summation methods allowing one to restore a function according to its Fourier-Walsh series. We also study the Besov space on a dyadic group in terms of the strong summability. Finally, we present necessary information about the Fourier- Walsh transform.