CALDERON COUPLES OF REARRANGEMENT-INVARIANT SPACES

We examine conditions under which a pair of rearrangement invariant function spaces on [0, 1] or [0, infinity) form a Calderon couple. A very general criterion is developed to determine whether such a pair is a Calderon couple, with numerous applications. We give, for example, a complete classification of those spaces X which form a Calderon couple with L(infinity). We specialize our results to Orlicz spaces and are able to give necessary and sufficient conditions on an Orlicz function F so that the pair (L(F), L(infinity)) forms a Calderon pair.