In this talk, we will introduce the general p-McCarthy-Bergman space \mathcal{A_{\alpha}^p} of Dirichlet series and study the function theory on them.

We will study the boundedness of generalized Hilbert operators H_g on\mathcal{A_{\alpha}^p}.Particularly, it is shown that H_g is bounded on \mathcal{A_{\alpha}^p} if and only if g belongs to a mean Lipschitz space of Dirichlet series.Furthermore, the Volterra operator on \mathcal{A_{\alpha}^p}is also studied. This talk is based on a joint work with Prof. Kunyu Guo and Dr. Xiangdi Fu.