Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5129714 | Statistics & Probability Letters | 2017 | 5 Pages |
Abstract
Suppose that f is a martingale and let |f|â, S(f) denote the associated maximal and square functions. We prove that for any weight w we have |||f|â||L1(w)â¤C||S(f)||L1(wâ)with C=16(2+1)=38.62742â¦. The proof rests on the construction of an appropriate special function, enjoying certain size and concavity conditions. Furthermore, we show that the term wâ 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
Authors
Adam Osȩkowski,