Korenblum's principle for Bergman spaces with radial weights
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866916736134021120 |
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| author | Efraimidis, Iason Llinares, Adrián Vukotić, Dragan |
| author_facet | Efraimidis, Iason Llinares, Adrián Vukotić, Dragan |
| contents | We show that the Korenblum maximum (domination) principle is valid for weighted Bergman spaces $A^p_w$ with arbitrary (non-negative and integrable) radial weights $w$ in the case $1\le p<\infty$. We also notice that in every weighted Bergman space the supremum of all radii for which the principle holds is strictly smaller than one. Under the mild additional assumption $\liminf_{r\to 0^+} w(r)>0$, we show that the principle fails whenever $0<p<1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_14699 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Korenblum's principle for Bergman spaces with radial weights Efraimidis, Iason Llinares, Adrián Vukotić, Dragan Complex Variables 30H05 We show that the Korenblum maximum (domination) principle is valid for weighted Bergman spaces $A^p_w$ with arbitrary (non-negative and integrable) radial weights $w$ in the case $1\le p<\infty$. We also notice that in every weighted Bergman space the supremum of all radii for which the principle holds is strictly smaller than one. Under the mild additional assumption $\liminf_{r\to 0^+} w(r)>0$, we show that the principle fails whenever $0<p<1$. |
| title | Korenblum's principle for Bergman spaces with radial weights |
| topic | Complex Variables 30H05 |
| url | https://arxiv.org/abs/2307.14699 |