Mixed Lp$L^p$ estimates for transforms of noncommutative martingales

Abstract

Let . The paper is devoted to the study of estimates for transforms of noncommutative martingales, under the assumption that the transforming sequence takes values in , . This goes beyond the usual context of and studied so far in the literature. The obtained constants are of optimal order at the endpoints, in addition the approach allows to obtain sharp values in the range . The proof rests on real interpolation‐type arguments for martingale transforms, which are of independent interest.