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

Abstract

We show that the spaces E{ω}(Ω) 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 Rd. This result was previously shown by Bonet and Domański [2] under the additional assumptions that Ω is convex and ω satisfies the condition (α1). In particular, our work solves Problem 9.7 in [1].