Function cones and interpolation
Copyright policy )Function cones and interpolation
AbstractWe 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 (E0 ∩ Q,E1 ∩ Q)θ,p = (E0,E1)θ,p ∩ Q 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)
- University of Barcelona Spain
real interpolation, function cone, Interpolation between normed linear spaces, Abstract interpolation of topological vector spaces, linear and bilinear operators, Banach function space, Positive linear operators and order-bounded operators, K-functional, level set, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
real interpolation, function cone, Interpolation between normed linear spaces, Abstract interpolation of topological vector spaces, linear and bilinear operators, Banach function space, Positive linear operators and order-bounded operators, K-functional, level set, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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