On multipliers into martingale SL∞ spaces for arbitrary filtrations
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 m 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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