On sequence space representations of Hörmander–Beurling spaces

It is shown that Bloc p ,1/˜k (Ω) is isomorphic to (Bc p,k(Ω)) b (Ω open set in Rn, 1 p < ∞, k Beurling–Björck weight) extending a Hörmander’s result (the proof we give is valid in the vector-valued case, too). As a consequence, and using Vogt’s representation theorems and weighted Lp-spaces of entire analytic functions, a number of results on sequence space representations of Hörmander–Beurling are given.