A sharp BMO-BLO bound for the martingale maximal function

2 Jul 2021, 16:30


Leonid Slavin (University of Cincinnati)


We construct the exact Bellman function for the BMO-BLO action of the natural martingale maximal function for continuous-time martingales. (BLO stands for "bounded lower oscillation"; the natural maximal function is the one without the absolute value in the average). As consequences, we show that the BMO-BLO norm of the operator is 1 and also obtain a sharp weak-type inequality, which can be integrated to produce a broad range of sharp phi-estimates.

In an earlier work we found the corresponding Bellman function for alpha-regular discrete-time martingales, including the dyadic martingale. I will discuss the essential differences between the two cases. This is joint work with Adam Osekowski and Vasily Vasyunin.

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Leonid Slavin (University of Cincinnati)

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