On multipliers into martingale $SL^\infty$ spaces for arbitrary filtrations

Anton Tselishchev

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arXiv · 2303.08041

On multipliers into martingale $SL^\infty$ spaces for arbitrary filtrations

Anton Tselishchev

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Abstract

In this paper we study the following problem: for a given bounded positive function $f$ on a filtered probability space can we find another function (a multiplier) $m$, $0\le m\le 1$, such that the function $mf$ is not ``too small'' but its square function is bounded? We explicitly show how to construct such multipliers for the usual martingale square function and for so-called conditional square function. Besides that, we show that for the usual square function more general statement can be obtained by application of a non-constructive abstract correction theorem by S. V. Kislyakov.

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BibTeX RIS

Anton Tselishchev. 2023-03-14. On multipliers into martingale $SL^\infty$ spaces for arbitrary filtrations. https://arxiv.org/abs/2303.08041

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