$L^q$-valued Burkholder-Rosenthal inequalities and sharp estimates for stochastic integrals

Abstract

We prove sharp maximal inequalities for $L^q$-valued stochastic integrals with respect to any Hilbert space-valued local martingale. Our proof relies on new Burkholder-Rosenthal type inequalities for martingales taking values in an $L^q$-space.