A linear topological invariant for spaces of quasianalytic functions of Roumieu type

Abstract

We show that the spaces ${\mathcal{E}}_{\{\omega \}}(\mathrm{\Omega })$ of ultradifferentiable functions of Roumieu type satisfy the dual interpolation estimate for small theta, where ω is a quasianalytic weight function and Ω is an arbitrary open subset of ${\mathbb{R}}^d$. This result was previously shown by Bonet and Domański [2] under the additional assumptions that Ω is convex and ω satisfies the condition $({\alpha }_1)$. In particular, our work solves Problem 9.7 in [1].