A Carlson type inequality with blocks and interpolation

Kruglyak, Natan ; Maligranda, Lech ; Persson, Lars

Studia Mathematica, Tome 104 (1993), p. 161-180 / Harvested from The Polish Digital Mathematics Library

Résumé

An inequality, which generalizes and unifies some recently proved Carlson type inequalities, is proved. The inequality contains a certain number of “blocks” and it is shown that these blocks are, in a sense, optimal and cannot be removed or essentially changed. The proof is based on a special equivalent representation of a concave function (see [6, pp. 320-325]). Our Carlson type inequality is used to characterize Peetre’s interpolation functor $⟨⟩_{φ}$ (see [26]) and its Gagliardo closure on couples of functional Banach lattices in terms of the Calderón-Lozanovskiǐ construction. Our interest in this functor is inspired by the fact that if $φ = t^{θ}(0 < θ < 1)$, then, on couples of Banach lattices and their retracts, it coincides with the complex method (see [20], [27]) and, thus, it may be regarded as a “real version” of the complex method.

Détail

Publié le : 1993-01-01

Zbl 0824.46088

EUDML-ID : urn:eudml:doc:215967

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