Strong differential subordinates for noncommutative submartingales
Strong differential subordinates for noncommutative submartingales
We introduce a notion of strong differential subordination of noncommutative semimartingales, extending Burkholder's definition from the classical case (Ann.Probab.22 (1994) 995-1025).Then we establish the maximal weak-type (1, 1) inequality under the additional assumption that the dominating process is a submartingale.The proof rests on a significant extension of the maximal weak-type …