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ArticleOriginal scientific text

Title

Interpolation on families of characteristic functions

Authors 1, 2

Affiliations

  1. Department of Mathematics, Technion, Israel Institute of Technology, Haifa 32000, Israel
  2. Department of Mathematics, Ohio University, Athens, Ohio 45701, U.S.A.

Abstract

We study a problem of interpolating a linear operator which is bounded on some family of characteristic functions. A new example is given of a Banach couple of function spaces for which such interpolation is possible. This couple is of the form Φ¯=(B,L∞) where B is an arbitrary Banach lattice of measurable functions on a σ-finite nonatomic measure space (Ω,Σ,μ). We also give an equivalent expression for the norm of a function ⨍ in the real interpolation space (B,L∞)θ,p in terms of the characteristic functions of the level sets of ⨍.

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Studia Mathematica
2000/138/3
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Pages:
209-224
Main language of publication
English
Received
1998-08-19
Published
1999-11-30
Exact and natural sciences