Some Banach spaces of Dirichlet series

We study some L^p spaces of Dirichlet series, particularly two families of Bergman spaces A^p and B^p. We recover classical properties of spaces of analytic functions: boundedness of point evaluation, embeddings between these spaces and "Littlewood-Paley" formulas when p=2. We also show that the B^p spaces have properties similar to the classical Bergman spaces of the unit disk while the A^p spaces have a different behavior.