Schatten class composition operators on the Hardy space of Dirichlet series and a comparison-type principle
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Frédéric Bayart [2]
;
Athanasios Kouroupis
[1]
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[1] Norwegian University of Science and Technology
Norwegian University of Science and Technology
Noruega
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[2] Université Clermont Auvergne, Aubiere, France
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- Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 40, Nº 5, 2024, págs. 1863-1886
- Idioma: inglés
- DOI: 10.4171/RMI/1474
- Enlaces
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Resumen
We give necessary and sufficient conditions for a composition operator with Dirichlet series symbol to belong to the Schatten classes Sp of the Hardy space H2 of Dirichlet series. For p≥2, these conditions lead to a characterization for the subclass of symbols with bounded imaginary parts. Finally, we establish a comparison-type principle for composition operators. Applying our techniques in conjunction with classical geometric function theory methods, we prove the analogue of the polygonal compactness theorem for H2 and we give examples of bounded composition operators with Dirichlet series symbols on H p , p>0.
