Strong Factorizations between Couples of Operators on Banach Function Spaces

Let T : X1 → Y1 and S : X2 → Y2 be two continuous linear operators between Banach function spaces related to a finite measure space. Under some lattice requirements on the spaces involved, we give characterizations by means of inequalities of when T can be strongly factorized through S, that is, T = Mg ◦ S ◦Mf with Mf : X1 → X2 and Mg : Y2 → Y1 being multiplication operators defined by some measurable functions f and g. In particular, we study the cases when S is a composition operator or a kernel operator.