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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2401.09996 |
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| _version_ | 1866909076650196992 |
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| author | Carando, Daniel Defant, Andreas Marceca, Felipe Schoolmann, Ingo Sevilla-Peris, Pablo |
| author_facet | Carando, Daniel Defant, Andreas Marceca, Felipe Schoolmann, Ingo Sevilla-Peris, Pablo |
| contents | For a general Dirichlet series $\sum a_n e^{-λ_n s}$ with frequency $λ=(λ_n)_n$, we study how horizontal translation (i.e. convolution with a Poisson kernel) improves its integrability properties. We characterize hypercontractive frequencies in terms of their additive structure answering some questions posed by Bayart. We also provide sharp bounds for the strips $S_p(λ)$ that encode the minimum translation necessary for series in the Hardy space $\mathcal{H}_p(λ)$ to have absolutely convergent coefficients. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_09996 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hypercontractivity and strips of convergence in Hardy spaces of general Dirichlet series Carando, Daniel Defant, Andreas Marceca, Felipe Schoolmann, Ingo Sevilla-Peris, Pablo Functional Analysis 43A17, 30B50, 30H10 For a general Dirichlet series $\sum a_n e^{-λ_n s}$ with frequency $λ=(λ_n)_n$, we study how horizontal translation (i.e. convolution with a Poisson kernel) improves its integrability properties. We characterize hypercontractive frequencies in terms of their additive structure answering some questions posed by Bayart. We also provide sharp bounds for the strips $S_p(λ)$ that encode the minimum translation necessary for series in the Hardy space $\mathcal{H}_p(λ)$ to have absolutely convergent coefficients. |
| title | Hypercontractivity and strips of convergence in Hardy spaces of general Dirichlet series |
| topic | Functional Analysis 43A17, 30B50, 30H10 |
| url | https://arxiv.org/abs/2401.09996 |