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ArticleOriginal scientific text

Title

A Carlson type inequality with blocks and interpolation

Authors 1, 2, 2

Affiliations

  1. Department of Mathematics, Yaroslavl State University, Sovetskaya 14, 150 000 Yaroslavl, Russia
  2. Department of Mathematics, Luleå University, S-951 87 Luleå, Sweden

Abstract

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=tθ(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.

Keywords

ENG
concavity, Carlson's inequality, blocks, interpolation, Peetre's interpolation functor, Calderón-Lozanovskiǐ construction

Bibliography

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Studia Mathematica
1993/104/2
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Pages:
161-180
Main language of publication
English
Received
1992-05-13
Published
1993
Exact and natural sciences