Hardy-type inequalities on strong and weak Orlicz-Lorentz spaces

In the present paper, the characterization of strong-type modular inequality $$ int_0^infty {varphi (Sf(t))w(t)dt leqslant } int_0^infty {varphi (Cf(t))w(t)dt,forall f downarrow } $$ is given, where ?? ?? ???? and S is a Hardy operator. Furthermore, the equivalent conditions of modular inequalities and norm inequalities related to weak Orlicz-Lorentz spaces are researched. We also explore the conditions for Orlicz-Lorentz spaces and weak Orlicz-Lorentz spaces to be normable. Finally, the weak boundedness of certain Hardy-type operators on Orlicz-Lorentz spaces is studied.