Lizorkin-Freitag Formula for Several Weighted Lp Spaces and Vector-Valued Interpolation

A complete description of the real interpolation space L=(Lp0(ω0),…,Lpn(ωn))θ ,q is given. An interesting feature of the result is that the whole measure space (Ω,μ) can be divided into disjoint pieces Ωi (i∈I) such that L is an lq sum of the restrictions of L to Ωi, and L on each Ωi is a result of interpolation of just two weighted Lp spaces. The proof is based on a generalization of some recent results of the first two authors concerning real interpolation of vector-valued spaces.