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Interpolation on families of characteristic functions

Michael Cwikel, Archil Gulisashvili (2000)

Studia Mathematica

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...

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