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Interpolation on families of characteristic functions

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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 $\overline Φ =(B,L^∞)$ 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 ⨍.
Słowa kluczowe
  • Department of Mathematics, Technion, Israel Institute of Technology, Haifa 32000, Israel
  • Department of Mathematics, Ohio University, Athens, Ohio 45701, U.S.A.
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