On some iterated weighted spaces

It is proved that the Hörmander Bloc p,k(Ω1 × Ω2) and Bloc p,k1 (Ω1,Bloc p,k2 (Ω2)) spaces (Ω1 ⊂ Rn, Ω2 ⊂ Rm open sets, 1 p < ∞, ki Beurling–Björck weights, k = k1 ⊗ k2) are isomorphic whereas the iterated spaces Bloc p,k1 (Ω1,Bloc q,k2 (Ω2)) and Bloc q,k2 (Ω2,Bloc p,k1 (Ω1)) are not if 1 < p = q < ∞. A similar result for weighted Lp-spaces of entire analytic functions is also obtained. Finally a result on iterated Besov spaces is given: Bs 2,q (Rn,Bs 2,q (Rm)) and Bs 2,q (Rn+m) are not isomorphic when 1