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Maximal operator of the Fejér means of triangular partial sums of two-dimensional Walsh–Fourier series
-
Ushangi Goginava
und
Ferenc Weisz
Veröffentlicht/Copyright:
29. Februar 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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Schlagwörter für diesen Artikel
Walsh function;
Hardy space;
maximal operator;
triangular partial sums
Artikel in diesem Heft
- Masthead
- Stability estimates for the multidimensional elliptic obstacle problem
- On the two-point boundary value problems for linear impulsive systems with singularities
- Explicit solutions of the boundary value problems of the theory of consolidation with double porosity for the half-plane
- Convergence of modification of the Durrmeyer type -Baskakov operators
- Backward stochastic differential equations with a convex generator
- On some ideal defined by density topology in the Cantor set
- Maximal operator of the Fejér means of triangular partial sums of two-dimensional Walsh–Fourier series
- Fixed point theorems for hybrid mappings satisfying an integral type contractive condition
- On the nonexistence of blowing-up solutions to a fractional functional-differential equation
- Two-weight inequalities for multilinear maximal operators
- An asymptotic model of a nonlinear adaptive orthotropic elastic rod
- Approximation of functions on locally compact abelian groups
