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 ).

A weak type inequality for the two-dimensional diagonal Sunouchi operator on the Hardy space

2011 ◽  
Vol 18 (1) ◽  
pp. 67-81
Author(s):  
Ushangi Goginava
Keyword(s):  
Fourier Series ◽  
Hardy Space ◽  
Weak Type ◽  
Type Inequality ◽  
Partial Sums ◽  
Two Dimensional ◽  
Fejér Means ◽  
Weak Type Inequality

Abstract Define the two dimensional diagonal Sunouchi operator where S 2 n , 2 n ƒ and σ 2 n ƒ are the (2 n , 2 n )th cubic-partial sums and 2 n th Marcinkiewicz–Fejér means of a two-dimensional Walsh–Fourier series. The main aim of this paper is to prove that the operator is bounded from the Hardy space H 1/2 to the weak L 1/2 space and is not bounded from the Hardy space H 1/2 to the space L 1/2.

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 → ∞.

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.

Modulus of continuity and convergence of subsequences of Vilenkin–Fejér means in martingale Hardy spaces

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Giorgi Tutberidze
Keyword(s):  
Hardy Space ◽  
Modulus Of Continuity ◽  
Hardy Spaces ◽  
Lebesgue Space ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Fejér Means ◽  
Necessary And Sufficient

Abstract In this paper, we find a necessary and sufficient condition for the modulus of continuity for which subsequences of Fejér means with respect to Vilenkin systems are bounded from the Hardy space H p {H_{p}} to the Lebesgue space L p {L_{p}} for all 0 < p < 1 2 {0<p<\frac{1}{2}} .

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