Abstract
Let X=(Xt)t≥0∈H1 and Y=(Yt)t≥0∈BMO be arbitrary continuous-path martingales. The paper contains the proof of the inequality E∫∞0|d⟨X,Y⟩t|≤√2‖X‖H1‖Y‖BMO2, 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
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
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