Maximal operators of Walsh–Kaczmarz logarithmic means

Abstract

The main aim of this article is to investigate the (H _p , L _p )-type inequality for the maximal operators of Riesz and Nörlund logarithmic means of Walsh–Kaczmarz–Fourier series. Moreover, we show that the behaviour of Nörlund logarithmic means is worse than the behaviour of Riesz logarithmic means in our special sense.

Keywords:

• Walsh–Kaczmarz system
• Hardy space
• logarithmic means
• Nörlund means

AMS Subject Classifications::

• 42C10
• 42B25