Composition operators and embedding theorems for some function spaces of Dirichlet series
Journal article, Peer reviewed
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Date
2019Metadata
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- Institutt for matematiske fag [2533]
- Publikasjoner fra CRIStin - NTNU [38576]
Abstract
We observe that local embedding problems for certain Hardy and Bergman spaces of Dirichlet series are equivalent to boundedness of a class of composition operators. Following this, we perform a careful study of such composition operators generated by polynomial symbols \varphi on a scale of Bergman-type Hilbert spaces \mathscr {D}_\alpha. We investigate the optimal \beta such that the composition operator \mathscr {C}_\varphi maps \mathscr {D}_\alpha boundedly into \mathscr {D}_\beta. We also prove a new embedding theorem for the non-Hilbertian Hardy space \mathscr {H}^p into a Bergman space in the half-plane and use it to consider composition operators generated by polynomial symbols on \mathscr {H}^p, finding the first non-trivial results of this type. The embedding also yields a new result for the functional associated to the multiplicative Hilbert matrix.