  We study the boundary behavior of functions in the Hardy spaces HD^p for
ordinary Dirichlet series. Our main result, answering a question of H.
Hedenmalm, shows that the classical F. Carlson theorem on integral means does
not extend to the imaginary axis for functions in HD^\infty, i.e., for ordinary
Dirichlet series in H^\infty of the right half-plane. We discuss an important
embedding problem for HD^p, the solution of which is only known when p is an
even integer. Viewing HD^p as Hardy spaces of the infinite-dimensional
polydisc, we also present analogues of Fatou's theorem.
