Calderon-Lozanovskii construction on weighted Banach function lattices

[摘要] We show that the Calderon-Lozanovskii construction phi(.) commute with arbitrary weighted Banach function lattices, that is, phi(E-0(w(0)), E-1(w(1))) = phi(E-0, E-1)(w) with w = 1/phi(1/w(0), 1/w(1)) if and only if phi is equivalent to a power function. From this result we can also get the Stein-Weiss theorem on interpolation of weighted L-p spaces and its generalizations. (C) 2003 Elsevier Inc. All rights reserved.

[发布日期] 2003-12-15

[关键词] Calderon-Lozanovskii spaces;Banach function lattices;weighted spaces;weights;quasi-banach function lattices;complex interpolation method