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Article Dans Une Revue Mathematische Zeitschrift Année : 2019

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

Ole Fredrik Brevig
  • Fonction : Auteur

Résumé

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 ϕ on a scale of Bergman–type Hilbert spaces Dα. We investigate the optimal β such that the composition operator Cϕ maps Dα boundedly into Dβ. We also prove a new embedding theorem for the non-Hilbertian Hardy space H p into a Bergman space in the half-plane and use it to consider composition operators generated by polynomial symbols on 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.
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hal-04605902 , version 1 (08-06-2024)

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Frédéric Bayart, Ole Fredrik Brevig. Composition operators and embedding theorems for some function spaces of Dirichlet series. Mathematische Zeitschrift, 2019, 293 (3-4), pp.989-1014. ⟨10.1007/s00209-018-2215-x⟩. ⟨hal-04605902⟩
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