2023/03/14 by Tselishchev, Anton
#46B10 #60G42 #60G46 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR)
paper · doi:10.48550/arxiv.2303.08041
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.