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

Author

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  • Brzozowski, Michał
  • Osękowski, Adam

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.

Suggested Citation

  • Brzozowski, Michał & Osękowski, Adam, 2019. "Sharp weighted weak type (∞,∞) inequality for differentially subordinate martingales," Statistics & Probability Letters, Elsevier, vol. 155(C), pages 1-1.
    • Handle: RePEc:eee:stapro:v:155:y:2019:i:c:8
    DOI: 10.1016/j.spl.2019.108561
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