Speaker
Leonid Slavin
(University of Cincinnati)
Description
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.
Primary author
Leonid Slavin
(University of Cincinnati)
