Calderón couples of Lipschitz spaces (Q1897282)

Two real interpolation functors \(F_0\), \(F_1\) are said to form a \(C\)-pair if \((F_0 (\overline {X}), F_1 (\overline {X}))\) is a Calderón couple for every Banach couple \(\overline {X}\). The authors give a necessary condition for \(F_0\) and \(F_1\) to form a \(C\)-pair in terms of the fundamental functions of these functors. This condition turns out to be sufficient for the functors defined by weighted \(L_p\)- parameters. As a corollary they give a complete description of all Calderón couples of Lipschitz spaces. Some new results are also obtained for couples of Lorentz spaces.