We prove inequalities involving noncommutative differentially subordinate martingales.
Central South University, Changsha, China
Thu, 25/10/2018 - 12:00pm
RC-4082, The Red Centre, UNSW
More precisely, we prove that if xx is a self-adjoint noncommutative martingale and yy is weakly differentially subordinate to xx then yy admits a decomposition y=z+wy=z+w where zz and ww are two martingales such that:
We also prove strong-type (p,p)(p,p) version of the above weak-type result for 1<p<21<p<2. As a byproduct of our approach, we obtain new and constructive proof of the noncommutative Burkholder-Gundy inequalities for 1<p<21<p<2 with the optimal order of the constants as p→1p→1.