On the maximal operator of $(C, α)$-means of Walsh–Kaczmarz–Fourier series

• Date: 2010
• Main Authors: Goginava, U., Nagy, К., Гогінава, У., Надь, К.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2010
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2852
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

Simon [J. Approxim. Theory, 127, 39–60 (2004)] proved that the maximal operator $σ^{α,κ,*}$ of the $(C, α)$-means of the Walsh–Kaczmarz–Fourier series is bounded from the martingale Hardy space $H_p$ to the space $L_p$ for $p > 1 / (1 + α), \;0 < α ≤ 1$. Recently, Gát and Goginava have...