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 Doma\'nski [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].
Categories: math.FA