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Acta Mathematica Hungarica
Volume/Issue:
Volume 115: Issue 4
DOI:
https://doi.org/10.1007/s10474-007-5268-6
Author:
U. Goginava

Abstract  

The main aim of this paper is to prove that the maximal operator
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\sigma _0^* : = \mathop {\sup }\limits_n \left| {\sigma _{n,n} } \right|$$ \end{document}
of the Fejr mean of the double Walsh-Fourier series is not bounded from the Hardy space H 1/2 to the space weak-L 1/2.
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Acta Mathematica Hungarica
Volume/Issue:
Volume 121: Issue 4
DOI:
https://doi.org/10.1007/s10474-008-7219-2
Author:
U. Goginava

Abstract  

The aim of this paper is to prove that for an arbitrary set of measure zero there exists a bounded function for which the Fejér means of the Walsh-Fourier series of the function diverge.

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Periodica Mathematica Hungarica
Volume/Issue:
Volume 59: Issue 2
DOI:
https://doi.org/10.1007/s10998-009-0173-0
Author:
Ushangi Goginava

Abstract  

The main aim of this paper is to prove that there exists a martingale f ∈ H 1 2/▭ such that the restricted maximal operators of Fejér means of twodimensional Walsh-Fourier series and conjugate Walsh-Fourier series does not belong to the space weak-L 1/2.

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Studia Scientiarum Mathematicarum Hungarica
Volume/Issue:
Volume 49: Issue 2
DOI:
https://doi.org/10.1556/sscmath.49.2012.2.1196
Authors:
Ushangi Goginava
and
Larry Gogoladze

In this paper we study the exponential uniform strong approximation of two-dimensional Walsh-Fourier series. In particular, it is proved that the two-dimensional Walsh-Fourier series of the continuous function f is uniformly strong summable to the function f exponentially in the power 1/2. Moreover, it is proved that this result is best possible.

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Studia Scientiarum Mathematicarum Hungarica
Volume/Issue:
Volume 49: Issue 2
DOI:
https://doi.org/10.1556/sscmath.49.2012.2.1202
Authors:
Ushangi Goginava
and
Ferenc Weisz

In this paper we characterize the set of convergence of the Marcinkiewicz-Fejér means of two-dimensional Walsh-Fourier series.

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Acta Mathematica Hungarica
Volume/Issue:
Volume 41: Issue 3-4
DOI:
https://doi.org/10.1007/bf01961307
Author:
K. Yoneda

References [1] Fine , N.J. 1949 On Walsh functions Trans. Amer. Math. Soc. 65 372 – 414 10

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Studia Scientiarum Mathematicarum Hungarica
Volume/Issue:
Volume 57: Issue 2
DOI:
https://doi.org/10.1556/012.2020.57.2.1459
Authors:
György Gát
and
Rodolfo Toledo

1 Introduction A system formed by Walsh functions is an orthonormal system which takes only values 1 and −1. This property, which is why the Walsh system was considered to be an “artificial” orthonormal system by many mathematicians in 1923, the

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Studia Scientiarum Mathematicarum Hungarica
Volume/Issue:
Volume 58: Issue 1
DOI:
https://doi.org/10.1556/012.2021.58.1.1483
Authors:
Nata Gogolashvili
and
George Tephnadze

, 7 ( 2 ): 141 – 150 , 1981 . [37] A . Šne˘ıder . On series of Walsh functions with monotonic coefficients . Izvestiya Akad. Nauk SSSR. Ser. Mat . 12 : 179 – 192 , 1948 . (In Russian.) [38] G . Tephnadze . On the maximal operators of Kaczmarz

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