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 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 in terms of the characteristic functions of the level sets of ⨍.
@article{bwmeta1.element.bwnjournal-article-smv138i3p209bwm,
author = {Michael Cwikel and Archil Gulisashvili},
title = {Interpolation on families of characteristic functions},
journal = {Studia Mathematica},
volume = {141},
year = {2000},
pages = {209-224},
zbl = {0958.46006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv138i3p209bwm}
}
Cwikel, Michael; Gulisashvili, Archil. Interpolation on families of characteristic functions. Studia Mathematica, Tome 141 (2000) pp. 209-224. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv138i3p209bwm/
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