\(L^ p\)-norm convergence of series in compact, totally disconnected groups
The authors study Fourier series on ``non-Abelian'' Vilenkin groups, i.e., totally disconnected, infinite compact groups whose topology satisfies a countability axiom. The main result is that when such a group is of bounded type, the Fourier series of any \(f\in L^p\), \(1\leq p\leq \infty\), is Cesàro summable to \(f\) in \(L^p\) norm. This generalizes the corresponding Abelian result which was obtained by \textit{J. Pál} and \textit{P. Simon} [Acta Math. Acad. Sci. Hung. 29, 155-164 (1977; Zbl 0345.42011)].
scientific article; zbMATH DE number 913003