On the boundedness of subsequences of Vilenkin-Fejér means on the martingale Hardy spaces

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

Georgian Mathematical Journal ◽

10.1515/gmj-2021-2106 ◽

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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A note on the norm convergence by Vilenkin–Fejér means

Georgian Mathematical Journal ◽

10.1515/gmj-2014-0051 ◽

2014 ◽

Vol 21 (4) ◽

Author(s):

George Tephnadze

Keyword(s):

Modulus Of Continuity ◽

Hardy Spaces ◽

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Norm Convergence ◽

Fejér Means ◽

Necessary And Sufficient

AbstractThe main aim of this paper is to find necessary and sufficient conditions for the convergence of Fejér means in terms of the modulus of continuity on the Hardy spaces

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On the maximal operators of Vilenkin-Fejér means on Hardy spaces

Mathematical Inequalities & Applications ◽

10.7153/mia-16-23 ◽

2013 ◽

pp. 301-312

Author(s):

George Tephnadze

Keyword(s):

Hardy Spaces ◽

Maximal Operators ◽

Fejér Means

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On the maximal operators of Fejér means with respect to the character system of the group of 2-adic integers in hardy spaces

Mathematical Notes ◽

10.1134/s0001434615070068 ◽

2015 ◽

Vol 98 (1-2) ◽

pp. 68-77

Author(s):

G. Gát ◽

K. Nagy

Keyword(s):

Hardy Spaces ◽

Maximal Operators ◽

Fejér Means ◽

Character System

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Brownian Motion, Hardy Spaces and Bounded Mean Oscillation

10.1017/cbo9780511662386 ◽

1977 ◽

Cited By ~ 17

Author(s):

K. E. Petersen

Keyword(s):

Brownian Motion ◽

Hardy Spaces ◽

Bounded Mean Oscillation ◽

Mean Oscillation

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HARDY SPACES, APPROXIMATION ISSUES AND BOUNDARY VALUE PROBLEMS

Eurasian Mathematical Journal ◽

10.32523/2077-9879-2018-9-3-85-94 ◽

2018 ◽

Vol 9 (3) ◽

pp. 85-94

Author(s):

V.I. Vlasov ◽

◽

Keyword(s):

Boundary Value Problems ◽

Hardy Spaces ◽

Boundary Value

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

Studia Scientiarum Mathematicarum Hungarica ◽

10.1556/sscmath.2008.1053 ◽

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 ).

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