Optimal Flat Functions in Carleman-Roumieu Ultraholomorphic Classes in Sectors.

We construct optimal flat functions in Carleman-Roumieu ultraholomorphic classes associated to general strongly nonquasianalytic weight sequences, and defined on sectors of suitably restricted opening. A general procedure is presented in order to obtain linear continuous extension operators, right inverses of the Borel map, for the case of regular weight sequences in the sense of Dyn'kin. Finally, we discuss some examples (including the well-known q -Gevrey case) where such optimal flat functions can be obtained in a more explicit way.