Calderَn Couples of Lipschitz Spaces

Two real interpolation functors F0, F1 are said to form a C-pair if (F0(X), F1(X)) is a Calderَ couple for every Banach couple X. We give a necessary condition for F0 and F1 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 Lp-parameters. As a corollary the complete description of all Calderَn couples of Lipschitz spaces is given. Some new results are also obtained for couples of Lorentz spaces.