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  • Author or Editor: Ushangi Goginava x
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The boundedness of the Marcinkiewicz maximal operator for double Vilenkin-Fourier series from the martingale Hardy-Lorentz space H p,q into the Lorentz space L p,q is studied.

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Abstract  

We investigate approximation properties of Cesàro (C; −α, −β)-means of double Walsh-Fourier series with α, β ∈ (0, 1). As an application, we obtain a sufficient condition for the convergence of the means σ n,m /−α,−β (f; x, y) to f(x,y) in the L p-metric, p ∈ [1, ∞]. We also show that this sufficient condition cannot be improved.

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The boundednes of (C,α)-means of the cubic partial sums of d-dimensional Walsh-Fourier series is studied from the martingale Hardy space H p into the space L p.

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Abstract  

The main aim of this paper is to prove that there exists a martingale fH 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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The main aim of this paper is to prove that the maximal operator σ * α of the (C, α) means of the cubical partial sums of the two-dimensional Walsh-Fourier series is bounded from the Hardy space H 2/(2+α) to the space weak-L 2/(2+α).

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The maximal Orlicz spaces such that the mixed logarithmic means of multiple Walsh-Fourier series for the functions from these spaces converge in measure and in norm are found.

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

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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 H 2/3 ( G 2 ) to the space L 2/3 ( G 2 ).

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Abstract  

The main aim of this paper is to prove that the maximal operator σ 0 k*:= supnσ n,n k∣ of the Fej�r means of double Fourier series with respect to the Kaczmarz system is not bounded from the Hardy space H 1/2 to the space weak-L 1/2.

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