Interpolation on families of characteristic functions
Studia Mathematica, Tome 138 (2000) no. 3, pp. 209-224
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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 ⨍.
@article{10_4064_sm_138_3_209_224,
author = {Michael Cwikel and },
title = {Interpolation on families of characteristic functions},
journal = {Studia Mathematica},
pages = {209--224},
publisher = {mathdoc},
volume = {138},
number = {3},
year = {2000},
doi = {10.4064/sm-138-3-209-224},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-138-3-209-224/}
}
TY - JOUR AU - Michael Cwikel AU - TI - Interpolation on families of characteristic functions JO - Studia Mathematica PY - 2000 SP - 209 EP - 224 VL - 138 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/sm-138-3-209-224/ DO - 10.4064/sm-138-3-209-224 LA - en ID - 10_4064_sm_138_3_209_224 ER -
Michael Cwikel; . Interpolation on families of characteristic functions. Studia Mathematica, Tome 138 (2000) no. 3, pp. 209-224. doi: 10.4064/sm-138-3-209-224
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