Function cones and interpolation



We consider interpolation of operators acting on functions that belong to a given cone Q with the so-called decomposition property. The set of all positive functions whose level sets are the level sets of a given function is the main example, and the cone of all decreasing functions is a particular case. As applications, we obtain conditions for the identity (E0Q,E1Q)θ,p = (E0,E1)θ,pQ and interpolation results for operators which are bounded when restricted to a given family of characteristic funcions. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)