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1

On the partial sums of Walsh-Fourier series

100%

Tephnadze G.

Colloquium Mathematicum

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2015

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tom 141

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nr 2

227-242

EN

We investigate convergence and divergence of specific subsequences of partial sums with respect to the Walsh system on martingale Hardy spaces. By using these results we obtain a relationship of the ratio of convergence of the partial sums of the Walsh series and the modulus of continuity of the martingale. These conditions are in a sense necessary and sufficient.

2

Walsh-Marcinkiewicz means and Hardy spaces

63%

Nagy K., Tephnadze G.

Open Mathematics

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2014

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tom 12

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nr 8

1214-1228

EN

The main aim of this paper is to investigate the Walsh-Marcinkiewicz means on the Hardy space H p, when 0 < p < 2/3. We define a weighted maximal operator of Walsh-Marcinkiewicz means and establish some of its properties. With its aid we provide a necessary and sufficient condition for convergence of the Walsh-Marcinkiewicz means in terms of modulus of continuity on the Hardy space H p, and prove a strong convergence theorem for the Walsh-Marcinkiewicz means.

3

Relations between some classes of functions of generalized bounded variation

51%

Gogatishvili A., Goginava U., Tephnadze G.

Banach Center Publications

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2014

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tom 102

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nr 1

89-98

EN

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

Ograniczanie wyników

1 Banach Center Publications

1 Colloquium Mathematicum

1 Open Mathematics

3 Tephnadze G.

1 Gogatishvili A.

1 Goginava U.

1 Nagy K.

1 2015

2 2014

On the partial sums of Walsh-Fourier series

Walsh-Marcinkiewicz means and Hardy spaces

Relations between some classes of functions of generalized bounded variation