On sequence space representations of Hörmander–Beurling spaces

Abstract

It is shown that B p ′ , 1 / k ˜ loc ( Ω ) is isomorphic to ( B p , k c ( Ω ) ) b ′ ( Ω open set in R n , 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 L p -spaces of entire analytic functions, a number of results on sequence space representations of Hörmander–Beurling are given.