A Note on Carleson-Hunt Type Theorems for Vilenkin-Fourier Series

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发表日期：

2024年

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L. -E. Persson,
F. Schipp,
G. Tephnadze,
F. Weisz

摘要

In this paper we discuss an analogy of the Carleson-Hunt theorem with respect to Vilenkin systems. In particular, we investigate the almost everywhere convergence of Vilenkin-Fourier series of \(f\in L_p(G_m)\) for \(p>1\) in case the Vilenkin system is bounded. Moreover, we state an analogy of the Kolmogorov theorem for \(p=1\) and construct a function \(f\in L_1(G_m)\) such that the partial sums with respect to Vilenkin systems diverge everywhere.