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Sharp Lorentz-norm estimates for BMO martingales

Łukasz Kamiński and Adam Osękowski

Statistics & Probability Letters, 2021, vol. 173, issue C

Abstract: Let X be a BMO martingale with continuous paths and let 2≤q≤p<∞ be given parameters. The paper contains the proof of the Lorentz-norm inequality ‖X∞‖p,q≤2−1∕pp∕q(q+1)∕qΓ(q+1)1∕q‖X‖BMO,and the constant is shown to be the best possible.

Keywords: BMO martingale; Lorentz norm; Best constant; Bellman function (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1016/j.spl.2021.109068

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