Littlewood--Paley--Rubio de Francia inequality for arbitrary Vilenkin systems

Rubio de Francia proved the one-sided version of Littlewood--Paley inequality for arbitrary intervals. In this paper, we prove the similar inequality in the context of arbitrary Vilenkin systems.Comment: 29 page

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

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.Comment: 15 page