Weighted Banach spaces of entire functions
It is proved that, given \(k> 0\) and \(p\in {\mathcal N}\), the Banach space \(E= H(e^{-k| z|^ p})_ 0({\mathcal C})\) of entire functions \(f\) such that \(| f(z)|= o(e^{k| z|^ p})\) is isomorphic to \(c_ 0\). An example of a rapidly decreasing continuous and radial weight \(v\) on \(\mathcal C\) such that the Banach space of entire functions \(f\) satisfying \(| f(z)|= o(v(z)^{-1})\) is not isomorphic to \(c_ 0\) is also included.
rapidly decreasing continuous and radial weight
scientific article; zbMATH DE number 743531