A Mandelbrojt region is a (not necessarily sectorial) connected open set $D$ in the Riemann surface of the logarithm with 0 in its boundary, symmetric with respect to a direction and with a positive opening (in a precise sense).

In 1952, S. Mandelbrojt gave a characterization of the injectivity of the asymptotic Borel mapping for the class of functions admitting uniform $\mathbb{M}$-asymptotic expansion in these domains, where the control of the remainders is specified in terms of a given weight sequence $\mathbb{M}$ of positive real numbers. We hope to extend this criterion to the Carleman-Roumieu ultraholomorphic class in $D$ consisting of the holomorphic functions with uniformly bounded derivatives in terms of the sequence $\mathbb{M}$.

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