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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

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.

The weak type inequality for the Walsh system

100%

Goginava U.

Studia Mathematica

2008

tom 185

nr 1

35-48

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 $L_{1/2}$.

Norm convergence of Fejér means of two-dimensional Walsh-Fourier series

100%

Goginava U.

Banach Center Publications

2011

tom 95

nr 1

317-324

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-$L_{1/2}$.

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

We prove inclusion relations between generalizing Waterman's and generalized Wiener's classes for functions of two variable.

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

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-$L_{1/2}$.