THE SEMIGROUP OF MARCINKIEWICZ MODULARS WITH INVOLUTION

摘要

The set M of all concave Marcinkiewicz modulars on [0,1] is a semigroup with respect to the usual composition of functions. We show that some properties of modulars (which are of importance in interpolation and in general Banach theory) distinguish subsets of M that form ideals of the semigroup. These ideals turn out to be in a natural duality relation, which is also studied.