Article ID Journal Published Year Pages File Type
5129714 Statistics & Probability Letters 2017 5 Pages PDF
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 0

Related Topics
Physical Sciences and Engineering Mathematics Statistics and Probability
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