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

Abstract

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

20 pages