Volterra operators and Hankel forms on Bergman spaces of Dirichlet series

2020/04/08 by Bommier-Hato, H.
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2004.04087

Abstract

For a Dirichlet series g, we study the Volterra operator Tg of symbol g, acting on a class of weighted Hilbert spaces of Dirichlet series. We obtain sufficient / necessary conditions for Tg to be bounded (resp. compact), involving BMO and Bloch type spaces on some half-plane. We also investigate the membership of Tg in Schatten classes. We also relate the boundedness of Tg to the boundedness of a multiplicative Hankel form of symbol g.

Related

• Volterra operator acting on Bergman spaces of Dirichlet series
• The generalized Volterra integral operator and Toeplitz operator on weighted Bergman spaces
• Volterra type integration operators from Bergman spaces to Hardy spaces
• Volterra type operators on weighted Dirichlet spaces
• Volterra-composition operators on the weighted Bergman space with exponential type weights