Given a frequency \(\lambda \), we study general Dirichlet series \(\sum a_n e^{-\lambda _n s}\). First, we give a new condition on \(\lambda \) which ensures that a somewhere convergent Dirichlet series defining a bounded holomorphic function in the right half-plane converges uniformly in this half-plane, improving classical results of Bohr and Landau. Then, following recent works of Defant and Schoolmann, we investigate Hardy spaces of these Dirichlet series. We get general results on almost sure convergence which have an harmonic analysis flavour. Nevertheless, we also exhibit examples showing that it seems hard to get general results on these spaces as spaces of holomorphic functions.

给定频率\(\lambda \)，我们研究一般狄利克雷级数\(\sum a_n e^{-\lambda _n s}\)。首先，我们在\(\lambda \)上给出了一个新条件，它确保在右半平面中定义有界全纯函数的某处收敛狄利克雷级数在该半平面中一致收敛，从而改进了 Bohr 和 Landau 的经典结果。然后，根据 Defant 和 Schoolmann 最近的工作，我们研究了这些狄利克雷级数的哈代空间。我们得到了几乎肯定收敛的一般结果，这些结果具有调和分析的味道。尽管如此，我们也展示了一些例子，表明在这些空间作为全纯函数空间似乎很难得到一般结果。