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1
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Convergence of logarithmic means of quadratic partial sums of double Fourier series

100%
Goginava U.
Colloquium Mathematicum
|
2013
|
tom 131
|
nr 1
99-112
EN
We investigate some convergence and divergence properties of the logarithmic means of quadratic partial sums of double Fourier series of functions, in measure and in the L Lebesgue norm.
2
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Norm convergence of Fejér means of two-dimensional Walsh-Fourier series

100%
Goginava U.
Banach Center Publications
|
2011
|
tom 95
|
nr 1
317-324
EN
The main aim of this paper is to prove that there exists a martingale $f ∈ H_{1/2}$ such that the Fejér means of the two-dimensional Walsh-Fourier series of f is not uniformly bounded in the space weak-$L_{1/2}$.
3
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The weak type inequality for the Walsh system

100%
Goginava U.
Studia Mathematica
|
2008
|
tom 185
|
nr 1
35-48
EN
The main aim of this paper is to prove that the maximal operator $σ^{#}$ is bounded from the Hardy space $H_{1/2}$ to weak-$L_{1/2}$ and is not bounded from $H_{1/2}$ to $L_{1/2}$.
4
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Maximal operators of Fejér means of double Vilenkin-Fourier series

51%
Blahota I., Gát G., Goginava U.
Colloquium Mathematicum
|
2007
|
tom 107
|
nr 2
287-296
EN
The main aim of this paper is to prove that the maximal operator $σ₀*: = supₙ|σ_{n,n}|$ of the Fejér means of the double Vilenkin-Fourier series is not bounded from the Hardy space $H_{1/2}$ to the space weak-$L_{1/2}$.
5
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Relations between some classes of functions of generalized bounded variation

51%
Gogatishvili A., Goginava U., Tephnadze G.
Banach Center Publications
|
2014
|
tom 102
|
nr 1
89-98
EN
We prove inclusion relations between generalizing Waterman's and generalized Wiener's classes for functions of two variable.
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