On some iterated weighted spaces

Abstract

[EN] It is proved that Hormander Bp,kloc (Omega 1 x Omega 2) and B-p,k1(loc) (Omega 1, B-p,k2(loc) (Omega(2))) spaces (Omega(1) subset of R-n, Omega(2) subset of R-m open sets, 1 <= p < infinity, k(i) Beurling-Bjorck weights, k = k(1) circle times k(2)) are isomorphic whereas the iterated spaces B-p,k1(loc) (Omega 1, B-p,k2(loc) (Omega(2))) and B-p,k2(loc) (Omega 1, B-p,k1(loc) (Omega(1))) are not if 1 < p not equal q < infinity. A similar result for weighted L-p-spaces of entire analytic functions is also obtained. Finally a result on iterated Besov spaces is given: B-2,q(s) (R-n, B-2,q(s) (R-m)) and B-2,q(s)(Rn+m) are not isomorphic when 1 < q not equal 2 < infinity. (c) 2007 Elsevier Inc. All rights reserved.