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A Carlson type inequality with blocks and interpolation

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Ya Kruglyak N., Maligranda L., Persson L. E.

Studia Mathematica

1993

tom 104

nr 2

161-180

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.

Ograniczanie wyników

1 Studia Mathematica

1 Maligranda L.

1 Persson L. E.

1 Ya Kruglyak N.

1 1993

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A Carlson type inequality with blocks and interpolation