Given a frequency $$\lambda $$ , we study general Dirichlet series $$\sum a_n e^{-\lambda _n s}$$ . First, give new condition on which ensures that somewhere convergent defining bounded holomorphic function in the right half-plane converges uniformly this half-plane, improving classical results of Bohr and Landau. Then, following recent works Defant Schoolmann, investigate Hardy spaces these se...