Noncommutative differentially subordinate martingales

2017-11-23


学术报告


报告人:焦勇 教授

中南大学 数学与统计学院

时  间1129日 周三 下午5:00 - 6:00

地  点:数学科学学院 第八教室

题  目:Noncommutative differentially subordinate martingales

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 Lp-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 these techniques will be useful in other situation as well.

简  介:焦勇, 中南大学“升华学者”特聘教授,博士生导师;湖南省杰青,国家优秀青年基金获得者。20096月博士毕业, 同时获得了武汉大学和法国弗朗什孔泰大学颁发的理学双博士学位;目前,以第一或通讯作者在《Probability Theory and Related Fields》、《JFA》、《Transactions of American Math Society》、《Journal of London Math Society》、《Indiana University Mathematics Journal》、《Proceedings of American Math Society》、《Journal of Operator Theory》、《Quarterly Journal of Mathematics》、《Studia Math》、《Journal of Mathematical Analysis and Applications》、《Nonlinear Analysis, Theory methods and Applications》、《Science China Math》、《Acta Mathematica Sinica》等国内外刊物上发表学术论文30多篇。


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