Sharp weighted weak type (∞,∞) inequality for differentially subordinate martingales

Michał Brzozowski and Adam Osękowski

Statistics & Probability Letters, 2019, vol. 155, issue C, -

Abstract: Let X=(Xt)t≥0 be a bounded, continuous-path martingale and Y=(Yt)t≥0 be a martingale that is differentially subordinate to X. We prove that if W is an A∞ weight of characteristic [W]A∞, then such that ||Y||weak(W)≤97[W]A∞||X||∞.Here weak(W) is the weak-L∞ space introduced by Bennett, DeVore and Sharpley. The linear dependence on [W]A∞ is shown to be best possible. The proof exploits certain special functions enjoying appropriate size conditions and concavity.

Keywords: Martingale; Weight; Burkholder’s function (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1016/j.spl.2019.108561

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