Calderón–Lozanovski˘ı construction on weighted Banach function lattices

We show that the Calderón–Lozanovski˘ı construction ϕ(·) commute with arbitrary weighted Banach function lattices, that is, ϕ(E0(w0),E1(w1)) = ϕ(E0,E1)(w) with w = 1/ϕ(1/w0, 1/w1) if and only if ϕ is equivalent to a power function. From this result we can also get the Stein–Weiss theorem on interpolation of weighted Lp spaces and its generalizations.  2003 Elsevier Inc. All rights reserved.