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Intersection properties for cones of monotone and convex functions with respect to the couple $(L_{p}, B M O)$

Inna Kozlov — 2001

Studia Mathematica

The paper is devoted to some aspects of the real interpolation method in the case of triples (X₀,X₁,Q) where X̅: = (X₀,X₁) 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...

Intersection properties for cones of nondecreasing concave functions

Inna Kozlov — 2005

Studia Mathematica

We prove that the basic facts of the real interpolation method remain true for couples of cones obtained by intersection of the cone of concave functions with rearrangement invariant spaces.

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Intersection properties for cones of monotone and convex functions with respect to the couple ( L p , B M O )

Intersection properties for cones of nondecreasing concave functions

Intersection properties for cones of monotone and convex functions with respect to the couple $(L_{p}, B M O)$