Composition operators and embedding theorems for some function spaces of Dirichlet series
| Autor: | Ole Fredrik Brevig, Frédéric Bayart |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Polynomial (hyperelastic model)
Mathematics::Functional Analysis Mathematics - Complex Variables Composition operator General Mathematics 010102 general mathematics Multiplicative function Hilbert space Mathematics::General Topology Hardy space Type (model theory) 01 natural sciences Mathematics - Functional Analysis Combinatorics symbols.namesake Primary 47B33. Secondary 30B50 30H10 30H20 Bergman space 0103 physical sciences symbols 010307 mathematical physics 0101 mathematics Dirichlet series Mathematics |
| Zdroj: | Mathematische Zeitschrift. 293:989-1014 |
| ISSN: | 1432-1823 0025-5874 |
| DOI: | 10.1007/s00209-018-2215-x |
| Popis: | 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 $\mathcal{D}_\alpha$. We investigate the optimal $\beta$ such that the composition operator $\mathcal{C}_\varphi$ maps $\mathcal{D}_\alpha$ boundedly into $\mathcal{D}_\beta$. We also prove a new embedding theorem for the non-Hilbertian Hardy space $\mathcal H^p$ into a Bergman space in the half-plane and use it to consider composition operators generated by polynomial symbols on $\mathcal{H}^p$, 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. Comment: This paper has been accepted for publication in Mathematische Zeitschrift |
| Databáze: | OpenAIRE |
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