B-Valued Martingale Hardy–Lorentz–Karamata Spaces

In this paper, we investigate the Hardy–Lorentz–Karamata spaces for Banach space-valued martingales. Relying on the geometrical properties of the underlying Banach spaces, we establish the atomic decompositions and characterize the dual spaces of these spaces. We also obtain some martingale inequalities in the setting of Hardy–Lorentz–Karamata spaces.