Real interpolation for martingale Orlicz-Lorentz-Karamata Hardy spaces

Abstract

We introduce a new class of Orlicz-Lorentz-Karamata spaces and develop the martingale theory in this framework. More precisely, we study the real interpolation theory for Orlicz-Lorentz-Karamata spaces as well as for the corresponding martingale Hardy spaces. As a consequence, the generalization of Doob's maximal inequality will be proved. Moreover, the atomic decompositions of the martingale Hardy Orlicz-Lorentz-Karamata spaces are also established. With the help of atomic decompositions, the duality and generalized John-Nirenberg theorem for martingale Hardy Orlicz-Lorentz-Karamata spaces are presented.