Integral means and boundary limits of Dirichlet series
Abstract
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 halfplane. 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 infinitedimensional polydisc, we also present analogues of Fatou's theorem.
 Publication:

arXiv eprints
 Pub Date:
 December 2007
 arXiv:
 arXiv:0712.0492
 Bibcode:
 2007arXiv0712.0492S
 Keywords:

 Mathematics  Complex Variables;
 Mathematics  Functional Analysis;
 30B50;
 42B30 (Primary);
 46E15;
 46J15 (Secondary)
 EPrint:
 13 pages