Calderón Couples of Lipschitz Spaces

Two real interpolation functors F 0, F 1 are said to form a C-pair if ( F 0( X ), F 1( X )) is a Calderó couple for every Banach couple X . We 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 the complete description of all Calderón couples of Lipschitz spaces is given. Some new results are also obtained for couples of Lorentz spaces.