时间： 2017.12.08 10:30-11:30
摘要：The classical differential subordination of martingales, introduced by Burkholder in the eighties, is generalized to the noncommutative setting. Then, working under this domination, we establish the strong-type inequalities with the constants of optimal order as $p\to 1$ and $p\to \infty$, and the corresponding end-point weak-type (1,1) estimate. In contrast to the classical case, we need to introduce two different versions of noncommutative differential subordination, depending on the range of the exponents. For the $L^p$-estimate, $2\leq p<\infty$ (the case of `big exponents'), a certain weaker version is sufficient; on the other hand, the strong-type $(p,p)$ inequality, $1<p<2$, and the weak-type (1,1) estimate (the cases of `small exponents') require a stronger version. As an application, we present a new proof of noncommutative Burkholder-Gundy inequalities. The main technique advance is a noncommutative version of a good $\lambda$-inequality and a certain summation argument. We expect that this techniques will be useful in other situation as well. This is a joint work with A. Osekowshi and Wu Lian.