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Open Access
August 2020 On the best constant in the martingale version of Fefferman’s inequality
Adam Osękowski
Bernoulli 26(3): 1912-1926 (August 2020). DOI: 10.3150/19-BEJ1175

Abstract

Let X=(Xt)t0H1 and Y=(Yt)t0BMO be arbitrary continuous-path martingales. The paper contains the proof of the inequality E0|dX,Yt|2XH1YBMO2, and the constant 2 is shown to be the best possible. The proof rests on the construction of a certain special function, enjoying appropriate size and concavity conditions.

Citation

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Adam Osękowski. "On the best constant in the martingale version of Fefferman’s inequality." Bernoulli 26 (3) 1912 - 1926, August 2020. https://doi.org/10.3150/19-BEJ1175

Information

Received: 1 July 2019; Revised: 1 November 2019; Published: August 2020
First available in Project Euclid: 27 April 2020

zbMATH: 07193947
MathSciNet: MR4091096
Digital Object Identifier: 10.3150/19-BEJ1175

Keywords: BMO , best constants , Duality , martingale , maximal

Rights: Copyright © 2020 Bernoulli Society for Mathematical Statistics and Probability

Vol.26 • No. 3 • August 2020
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