Almost Everywhere Convergence of Varying Parameter Setting Cesàro Means of Fourier Series With Respect to Walsh–Kaczmarz System

Abstract

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}}_{{{\alpha }_{n}},q}} of natural numbers and prove that the maximal operator supn ∈ ℕαn,qσnαnf\underset{n\,\in \,{{\mathbb{N}}_{{{\alpha }_{n}},q}}}{\mathop{\sup }}\,\left| \sigma _{n}^{{{\alpha }_{n}}}f \right| is of strong type (H1, L1), where H1 is a Hardy space.

Keywords

• 42c10
• cesàro means
• walsh–kaczmarz system
• fourier series
• almost everywhere convergence
• maximal operator
• hardy space