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Maximal operator of the Fejér means of triangular partial sums of two-dimensional Walsh–Fourier series
-
Ushangi Goginava
and
Ferenc Weisz
Published/Copyright:
February 29, 2012
Abstract.
It is proved that the maximal operator 
of the triangular-Fejér-means of a two-dimensional Walsh–Fourier series is
bounded from the dyadic Hardy space 
to 
for all
and, consequently, is of weak type (1,1). As a
consequence we obtain that the triangular-Fejér-means 
of a function 
converge a.e. to 
. The maximal operator 
is bounded from the Hardy space 
to the space weak-
and is not bounded from the Hardy space 
to the space 
.
Received: 2010-08-20
Published Online: 2012-02-29
Published in Print: 2012-March
© 2012 by Walter de Gruyter Berlin Boston
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