Some Banach spaces of Dirichlet series

Maxime Bailleul (1) , Pascal Lefèvre (1)

1 LML - Laboratoire de Mathématiques de Lens

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.

Mots clés: Dirichlet series; Bergman spaces; Hardy spaces; Riemann Zeta function

Domaines: Analyse fonctionnelle [math.FA]; Variables complexes [math.CV]

Maxime Bailleul, Pascal Lefèvre. Some Banach spaces of Dirichlet series. 2013. ⟨hal-00880265⟩