A Fefferman–Stein inequality for the martingale square and maximal functions

Adam Osȩkowski

Statistics & Probability Letters, 2017, vol. 129, issue C, 81-85

Abstract: Suppose that f is a martingale and let |f|∗, S(f) denote the associated maximal and square functions. We prove that for any weight w we have |||f|∗||L1(w)≤C||S(f)||L1(w∗)with C=16(2+1)=38.62742…. The proof rests on the construction of an appropriate special function, enjoying certain size and concavity conditions. Furthermore, we show that the term w∗ on the right cannot be replaced by the r-maximal function of w for any 0Keywords: Martingale; Maximal function; Square function; Best constant (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1016/j.spl.2017.05.008

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