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Norms of composition operators on the H2 space of Dirichlet series

Brevig, O. F. and Perfekt, K.-M. (2020) Norms of composition operators on the H2 space of Dirichlet series. Journal of Functional Analysis, 278 (2). 108320. ISSN 0022-1236

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To link to this item DOI: 10.1016/j.jfa.2019.108320


We consider composition operators $\mathscr{C}_\varphi$ on the Hardy space of Dirichlet series $\mathscr{H}^2$, generated by Dirichlet series symbols $\varphi$. We prove two different subordination principles for such operators. One concerns affine symbols only, and is based on an arithmetical condition on the coefficients of $\varphi$. The other concerns general symbols, and is based on a geometrical condition on the boundary values of $\varphi$. Both principles are strict, in the sense that they characterize the composition operators of maximal norm generated by symbols having given mapping properties. In particular, we generalize a result of J.~H.~Shapiro on the norm of composition operators on the classical Hardy space of the unit disc. Based on our techniques, we also improve the recently established upper and lower norm bounds in the special case that $\varphi(s) = c + r2^{-s}$. A number of other examples are given.

Item Type:Article
Divisions:Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:86293

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