The maximal function, an Orlicz-Lorentz subspace, and the multiplication operator

The Orlicz-Lorentz space is defined in terms of Young functions applied to the decreasing rearrangement of a function. In this article, we define a subspace of this space, using the maximal function, and study its structure as a Banach space. Additionally, we define a multiplication operator on these subspaces and characterize its most relevant properties.