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- W2529332987 abstract "Let W be a weight, i.e., a uniformly integrable, continuous-path martingale, and let W∗ denote the associated maximal function. We show that if X is an arbitrary càdlàg martingale and X∗, [X] denote its maximal and square functions, then ‖[X]1/2‖Lp(W)≤γp‖X∗‖Lp(W∗),1≤p≤2, where γp2=1+supt>1(2t−1)(1−tp−2)tp−1. The estimate is sharp for p∈{1,2}. Furthermore, it is proved that if p>2, then the above weighted inequality does not hold with any finite constant γp depending only on p." @default.
- W2529332987 created "2016-10-14" @default.
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- W2529332987 date "2017-01-01" @default.
- W2529332987 modified "2023-10-18" @default.
- W2529332987 title "Weighted inequalities for the martingale square and maximal functions" @default.
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- W2529332987 doi "https://doi.org/10.1016/j.spl.2016.09.020" @default.
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