Some Banach spaces of Dirichlet series

2013/11/15 by Bailleul, Maxime, Lefèvre, Pascal
#30H #46E15 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1311.3845

Abstract

The Hardy spaces of Dirichlet series denoted by \cal H^p (p≥1) have been studied in [12] when p = 2 and in [3] for the general case. In this paper we study some Lp-generalizations of spaces of Dirichlet series, particularly two families of Bergman spaces denoted \cal A^p and \cal 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 \cal B^p spaces have properties similar to the classical Bergman spaces of the unit disk while the \cal A^p spaces have a different behavior.

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• Hardy spaces of general Dirichlet series - a survey
• Hardy spaces of vector-valued Dirichlet series
• On the boundary behaviour of the Hardy spaces of Dirichlet series and a frame bound estimate
• Volterra operator acting on Bergman spaces of Dirichlet series
• Littlewood-type theorems for random Dirichlet series