Marcinkiewicz-Fejér Means of double VIlenkin-Fourier series

2007 ◽  
Vol 44 (1) ◽  
pp. 97-115
Author(s):  
Ushangi Goginava
Keyword(s):  
Fourier Series ◽  
Lorentz Space ◽  
Maximal Operator ◽  
Fejér Means

The boundedness of the Marcinkiewicz maximal operator for double Vilenkin-Fourier series from the martingale Hardy-Lorentz space Hp,q into the Lorentz space Lp,q is studied.

On the Marcinkiewicz-Fejér means of double Fourier series with respect to the Walsh-Kaczmarz system

2009 ◽  
Vol 46 (3) ◽  
pp. 399-421 ◽  
Author(s):  
György Gát ◽  
Ushangi Goginava ◽  
Károly Nagy
Keyword(s):  
Fourier Series ◽  
Lorentz Space ◽  
Maximal Operator ◽  
Double Fourier Series ◽  
Fejér Means

The main aim of this paper is to prove that the maximal operator of Marcinkiewicz-Fejér means of double Fourier series with respect to the Walsh-Kaczmarz system is bounded from the dyadic Hardy-Lorentz space Hpq into Lorentz space Lpq for every p > 2/3 and 0 < q ≦ ∞. As a consequence, we obtain the a.e. convergence of Marcinkiewicz-Fejér means of double Fourier series with respect to the Walsh-Kaczmarz system. That is, σn ( f, x1 , x2 ) → ( x1 , x2 ) a.e. as n → ∞.

The maximal operator of the Marcinkiewicz-Fejér means of the 2-dimensional Vilenkin-Fourier series

2008 ◽  
Vol 45 (3) ◽  
pp. 321-331
Author(s):  
István Blahota ◽  
Ushangi Goginava
Keyword(s):  
Fourier Series ◽  
Hardy Space ◽  
Maximal Operator ◽  
Fejér Means

In this paper we prove that the maximal operator of the Marcinkiewicz-Fejér means of the 2-dimensional Vilenkin-Fourier series is not bounded from the Hardy space H2/3 ( G2 ) to the space L2/3 ( G2 ).

scholarly journals Maximal operators of Fejér means of Walsh-Kaczmarz-Fourier series

2010 ◽  
Vol 8 (2) ◽  
pp. 181-200
Author(s):  
Ushangi Goginava ◽  
Károly Nagy
Keyword(s):  
Fourier Series ◽  
Maximal Operator ◽  
Maximal Operators ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Fejér Means

The main aim of this paper is to prove that there exists a martingalef∈H1/2such that the maximal Fejér operator with respect to Walsh-Kaczmarz system does not belong to the spaceL1/2. For the two-dimensional case, we prove that there exists a martingalef∈H1/2□(f∈H1/2)such that the restricted (unrestricted) maximal operator of Fejér means of two-dimensional Walsh-Kaczmarz-Fourier series does not belong to the space weak-L1/2.

On Some (H p,q , L p,q )-Type Maximal Inequalities with Respect to the Walsh–Paley System

2000 ◽  
Vol 7 (3) ◽  
pp. 475-488 ◽  
Author(s):  
U. Goginava
Keyword(s):  
Fourier Series ◽  
Lorentz Space ◽  
Positive Cone ◽  
Maximal Operators ◽  
Maximal Inequalities ◽  
Paley System

Abstract The boundedness of Cesáro maximal operators for multiple Walsh–Fourier series is studied from the martingale Hardy–Lorentz space Hpq into the Lorentz space Lpq . Supremum in the maximal operators is taken over a positive cone.

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