A note on weighted Banach spaces of holomorphic functions
The authors deal with weighted spaces of holomorphic functions. Let \(G\) be an open subset of \({\mathbb C}^N\) and \(v: G \to {\mathbb R}\) a continuous, strictly positive function, called a weight. Then the main result of the paper states that \[ (Hv)_0(G) = \{ f: G \to {\mathbb C} :\;f \text{ holomorphic, } v| f| \text{ vanishes at } \infty \} \] endowed with the weighted sup-norm \[ \| f\| _v = \sup_{z \in G } v(z) | f(z)| \] is always isomorphic to a subspace of \(c_0\). This was previously known only for very restricted classes of weights and open sets \(G\).
scientific article; zbMATH DE number 2051650