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On the maximal operator of Marcinkiewicz–Fejér means of the two-dimensional Walsh–Kaczmarz system
-
Károly Nagy
Published/Copyright:
May 15, 2013
Abstract.
In 2009, Goginava showed that
,
where 
is the 
th Marcinkiewicz–Fejér mean of
the Walsh–Kaczmarz–Fourier series, is not bounded from the Hardy space
to the space
. The main aim of this paper is to show that
the maximal operator
is bounded from the Hardy space to the space
. Moreover, it is proved that the order of deviant behavior of the th
Walsh–Kacmarz–Marcinkiewicz–Fejér mean is exactly 
.
Received: 2012-03-26
Accepted: 2013-03-27
Published Online: 2013-05-15
Published in Print: 2013-05-01
© 2013 by Walter de Gruyter Berlin Boston
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