We prove sectorial extension theorems for ultraholomorphic function classes of Beurling type defined by weight functions with a controlled loss of regularity. The proofs are based on a reduction lemma, due to the second author, which allows to extract the Beurling from the Roumieu case, which was treated recently by Jiménez-Garrido, Sanz, and the third author. To have control on the opening of the sectors, where the extensions exist, we use the (mixed) growth index and the order of quasianalyticity of weight functions. As a consequence, we obtain corresponding extension results for classes defined by weight sequences. Additionally, we give information on the existence of continuous linear extension operators.

我们证明了由权重函数定义的 Beurling 类型的超全纯函数类的扇区扩展定理，并具有受控的规律性损失。证明基于第二作者的归约引理，它允许从最近由 Jiménez-Garrido、Sanz 和第三作者处理的 Roumieu 案例中提取 Beurling。为了控制存在扩展的部门的开放，我们使用（混合）增长指数和权重函数的准分析阶数。因此，我们获得了由权重序列定义的类的相应扩展结果。此外，我们还提供了有关连续线性扩展算子存在的信息。