Interpolation orbits in couples of Lp spaces

We consider linear operators T mapping a couple of weighted L-p spaces {L-p0(U-0), L-p1(U-1)) into {L-q0(V-0),L-q1(V-1)) for any 1 less than or equal to p(0), p(1), q(0), q(1) < infinity, and describe the interpolation orbit of any a is an element of L-p0(U-0) + L-p1(U-1) that is we describe a space of all {Tal, where T runs over all linear bounded mappings from {L-p0(U-0), L-p1 (U-1)) into {L-q0(V-0),L-q1(V-1)). We show that interpolation orbit is obtained by the Lions-Peetre method of means with functional parameter as well as by the K-method with a weighted Orlicz space as a parameter. (C) 2002 Academie des science/Edition scientifiques et medicales Elsevier SAS.