Almost Everywhere Convergence of Varying Parameter Setting Cesàro Means of Fourier Series With Respect to Walsh–Kaczmarz System - Adimasu Anteneh Tilahun (Annales Mathematicae Silesianae)
In this paper, the almost everywhere convergence of Cesàro means of Walsh–Kaczmarz–Fourier series in a varying parameter setting is investigated. In particular, we define subsequence ℕαn,q{{\mathbb{N}}_{{{α }_{n}},q}} of natural numbers and prove that the maximal operator supn ∈ ℕαn,qσnαnf\underset{n\,\in \,{{\mathbb{N}}_{{{α }_{n}},q}}}{\mathop{\sup }}\,\left| σ _{n}^{{{α }_{n}}}f \right| is of strong type (H1, L1), where H1 is a Hardy space.