Intersection properties for cones of monotone and convex functions with respect to the couple (Lp, BMO)

The paper is devoted to some aspects of the real interpolation method in the case of triples (X-0, X-1, Q) where X := (X-0, X-1) is a Banach couple and Q is a convex cone. The first fundamental result of the theory, the interpolation theorem, holds in this situation (for linear operators preserving the cone structure). The second one, the reiteration theorem, holds only under some conditions on the triple. One of these conditions, the so-called intersection property, is studied for cones with respect to (L-P, BMO).