Properties of Besov and $Q_p$ spaces in terms of the Schwarzian derivative of harmonic mappings
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916361082503168 |
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| author | Arbeláez, Hugo Hernández, Rodrigo Sierra, Willy |
| author_facet | Arbeláez, Hugo Hernández, Rodrigo Sierra, Willy |
| contents | In this paper we give a characterization of $\log J_f$ belongs to $\widetilde{\mathcal{B}}_p$ or $\widetilde{\mathcal{Q}}_p$ spaces for any locally univalent sense-preserving harmonic mappings $f$ defined in the unit disk, using the Schwarzian derivative of $f$ and Carleson meseaure. In addition, we introduce the classes $\mathcal{BT}_p$ and $\mathcal{QT}_p$, based on the Jacobian operator, and begin a study of these. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_09062 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Properties of Besov and $Q_p$ spaces in terms of the Schwarzian derivative of harmonic mappings Arbeláez, Hugo Hernández, Rodrigo Sierra, Willy Complex Variables 30H25, 30H30, 31A05 In this paper we give a characterization of $\log J_f$ belongs to $\widetilde{\mathcal{B}}_p$ or $\widetilde{\mathcal{Q}}_p$ spaces for any locally univalent sense-preserving harmonic mappings $f$ defined in the unit disk, using the Schwarzian derivative of $f$ and Carleson meseaure. In addition, we introduce the classes $\mathcal{BT}_p$ and $\mathcal{QT}_p$, based on the Jacobian operator, and begin a study of these. |
| title | Properties of Besov and $Q_p$ spaces in terms of the Schwarzian derivative of harmonic mappings |
| topic | Complex Variables 30H25, 30H30, 31A05 |
| url | https://arxiv.org/abs/2408.09062 |