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arXiv · 1802.07669

On the convergence of partial sums with respect to Vilenkin system on the martingale Hardy spaces

G. Tephnadze
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Abstract

In this paper we derive characterizations of boundedness of the subsequences of partial sums with respect to Vilenkin system on the martingale Hardy spaces when $ 0<p<1 $. Moreover, we find necessary and sufficient conditions for the modulus of continuity of $f\in H_{p}$ martingales, which provide convergence of subsequences of partial sums on the martingale Hardy spaces. It is also proved that these results are the best possible in a special sense. As applications, both some well-known and new results are pointed out.

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G. Tephnadze. 2018-02-14. On the convergence of partial sums with respect to Vilenkin system on the martingale Hardy spaces. https://arxiv.org/abs/1802.07669

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