Title：Atomic decomposition for noncommutative martingales
Speaker：Zeqian Chen (Chinese Academy of Sciences)
Time：16:00-17:00, July24
Location：Tecent Meeting, Tecent Meeting ID: 397 718 094
Abstract：In this talk, we will report that an atomic type decomposition is proved for the noncommutative martingale Hardy space $\h_p$ for all $0<p<2$ by an explicit constructive method using algebraic atoms as building blocks. Using this elementary construction, we obtain a weaker form of the atomic decomposition of $\h_p$ for all $0< p < 1,$ and provide a constructive proof of the atomic decomposition for $1 \le p < 2.$ As application, we obtain a characterization of the dual space of the noncommutative martingale Hardy space $\h_p$ ($0<p<1$) as noncommutative Lipschitz space via the weaker form of the atomic decomposition. Our constructive method can also be applied to giving some sharp martingale inequalities. This is joint work with Narcisse Randrianantoanina and Quanhua Xu (许全华).
