Integral Means and Boundary Limits of Dirichlet Series
نویسنده
چکیده
We study the boundary behavior of functions in the Hardy spaces H 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 H ∞, i.e., for ordinary Dirichlet series in H∞ of the right half-plane. We discuss an important embedding problem for H , the solution of which is only known when p is an even integer. Viewing H p as Hardy spaces of the infinite-dimensional polydisc, we also present analogues of Fatou’s theorem.
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