Pascal Lefevre

The Hardy spaces of Dirichlet series $\mathcal{H}^p$ ($p\geq 1$) have been studied by Hedenmalm, Lindqvist and Seip when $p=2$ and by Bayart for the general values of $p$. We introduce the Orlicz version of Hardy spaces of Dirichlet series $\mathcal{H}^\psi$. We focus on the case $\psi=\psi_q(t)=\exp(t^q)-1$ and we compute the abscissa of convergence for these spaces, obtaining values interpolating the ones for $\mathcal{H}^p$ and $\mathcal{H}^\infty$. This solves a problem raised by Hedenmalm in 2002. This talk is a complement to the lectures of F. Bayart. Joint work with M. Bailleul and L. Rodr\'\i guez-Piazza.