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Composition operators and embedding theorems for some function spaces of Dirichlet series

Bayart, Frederic; Brevig, Ole Fredrik
Journal article, Peer reviewed
Accepted version
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URI
http://hdl.handle.net/11250/2626845
Date
2019
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  • Institutt for matematiske fag [2686]
  • Publikasjoner fra CRIStin - NTNU [41954]
Original version
Mathematische Zeitschrift. 2019, 1-26.   10.1007/s00209-018-2215-x
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.
Publisher
Springer Verlag
Journal
Mathematische Zeitschrift

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