Small Hankel operator induced by measurable symbol acting on weighted Bergman spaces
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916313612419072 |
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| author | Peláez, José Ángel Rättyä, Jouni |
| author_facet | Peláez, José Ángel Rättyä, Jouni |
| contents | The boundedness of the small Hankel operator $h^ω_{f}(g)=\overline{P_ω}(fg)$ induced by a measurable symbol $f$ and the Bergman projection $P_ω$ associated to a radial weight $ω$ acting from the weighted Bergman space $A^p_ω$ to its conjugate analytic counterpart $\overline{A^p_ω}$ is characterized on the range $1<p<\infty$ when $ω$ belongs to the class $\mathcal{D}$ of radial weights admitting certain two-sided doubling conditions. On the way to the proof a sharp integral estimate for certain modified Bergman kernels is obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_04645 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Small Hankel operator induced by measurable symbol acting on weighted Bergman spaces Peláez, José Ángel Rättyä, Jouni Complex Variables The boundedness of the small Hankel operator $h^ω_{f}(g)=\overline{P_ω}(fg)$ induced by a measurable symbol $f$ and the Bergman projection $P_ω$ associated to a radial weight $ω$ acting from the weighted Bergman space $A^p_ω$ to its conjugate analytic counterpart $\overline{A^p_ω}$ is characterized on the range $1<p<\infty$ when $ω$ belongs to the class $\mathcal{D}$ of radial weights admitting certain two-sided doubling conditions. On the way to the proof a sharp integral estimate for certain modified Bergman kernels is obtained. |
| title | Small Hankel operator induced by measurable symbol acting on weighted Bergman spaces |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2407.04645 |