Martingale inequalities on Musielak–Orlicz Hardy spaces

Abstract

AbstractGiven a probability space and a Musielak–Orlicz function , we investigate martingale inequalities in the framework of Musielak–Orlicz spaces by constructing atomic decompositions. Especially, the obtained results for Musielak–Orlicz functions with particular structure, including the variable Orlicz functions , , the variable double phase‐growth , and the perturbed variable exponent function are also new. Hence, we handle the martingale inequality for the above functional in a universal way.