On sequence space representations of Hörmander–Beurling spaces

AbstractIt is shown that Bp′,1/k˜loc(Ω) is isomorphic to (Bp,kc(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