Martingale decompositions and weak differential subordination in UMD Banach spaces

In this paper, we consider Meyer–Yoeurp decompositions for UMD Banach space-valued martingales. Namely, we prove that X is a UMD Banach space if and only if for any fixed p ∈ (1, ∞), any X-valued L^p-martingale M has a unique decomposition M = M^d + M^c such that M^d is a purely discontinuous martingale...