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

• Published in: Український математичний журнал
• Date: 2010
• Main Authors: Goginava, U., Nagy, K.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2010
• Subjects: Статті
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/164653
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: On the maximal operator of (C, α)-means of Walsh–Kaczmarz–Fourier series / U. Goginava, K. Nagy // Український математичний журнал. — 2010. — Т. 62, № 2. — С. 158–166. — Бібліогр.: 11 назв. — англ.

Simon [J. Approxim. Theory, 127, 39–60 (2004)] proved that the maximal operator σα,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 proved that this bound...