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The E and K functionals for the pair (X (A), l∞(B)).

Stefan Ericsson (1997)

Collectanea Mathematica

We prove some exact formulas for the E and K functionals for pairs of the type (X(A),l sub ∞ (B)) where X has the lattice property. These formulas are extensions of their well-known counterparts in the scalar valued case. In particular we generalize formulas by Pisier and by the present author.

The Lions's problem for Gustavsson-Peetre functor.

E.I. Bereznoi, Mieczyslaw Mastylo (1990)

Publicacions Matemàtiques

The problem of coincidence of the interpolation spaces obtained by use of the interpolation method of Gustavsson-Peetre generated by (parameters) quasi-concave functions is investigated. It is shown that a restriction of this method to the class of all non-trivial Banach couples gives different interpolation spaces whenever two different parameters satisfying some conditions are used.

Weak-type operators and the strong fundamental lemma of real interpolation theory

N. Krugljak, Y. Sagher, P. Shvartsman (2005)

Studia Mathematica

We prove an interpolation theorem for weak-type operators. This is closely related to interpolation between weak-type classes. Weak-type classes at the ends of interpolation scales play a similar role to that played by BMO with respect to the L p interpolation scale. We also clarify the roles of some of the parameters appearing in the definition of the weak-type classes. The interpolation theorem follows from a K-functional inequality for the operators, involving the Calderón operator. The inequality...

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