Muckenhoupt type weights and Berezin formulas for Bergman spaces
By means of Muckenhoupt type conditions, we characterize the weights $\omega$ on $\C$ such that the Bergman projection of $F^{2,\ell}_{\alpha}=H(\C)\cap L^2(\C,e^{-\frac{\alpha}2|z|^{2\ell}})$, $\alpha>0$, $\ell>1$, is bounded on $L^p(\C,e^{-\frac{\alpha p}2|z|^{2\ell}}\omega(z))$, for $1<p...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2445/184095 |
| Acceso en línea: | https://hdl.handle.net/2445/184095 |
| Access Level: | acceso abierto |
| Palabra clave: | Representacions integrals Nuclis de Bergman Operadors de Toeplitz Integral representations Bergman kernel functions Toeplitz operators |
| Sumario: | By means of Muckenhoupt type conditions, we characterize the weights $\omega$ on $\C$ such that the Bergman projection of $F^{2,\ell}_{\alpha}=H(\C)\cap L^2(\C,e^{-\frac{\alpha}2|z|^{2\ell}})$, $\alpha>0$, $\ell>1$, is bounded on $L^p(\C,e^{-\frac{\alpha p}2|z|^{2\ell}}\omega(z))$, for $1<p<\infty$. We also obtain explicit representation integral formulas for functions in the weighted Bergman spaces $A^p(\omega)=H(\C)\cap L^p(\omega)$. Finally, we check the validity of the so called Sarason conjecture about the boundedness of products of certain Toeplitz operators on the spaces $F^{p,\ell}_\alpha=H(\C)\cap L^p(\C,e^{-\frac{\alpha p}2|z|^{2\ell}})$. |
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