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Title: | Muckenhoupt type weights and Berezin formulas for Bergman spaces |
Author: | Cascante, Ma. Carme (Maria Carme) Fàbrega Casamitjana, Joan Pascuas Tijero, Daniel |
Keywords: | Representacions integrals Nuclis de Bergman Operadors de Toeplitz Integral representations Bergman kernel functions Toeplitz operators |
Issue Date: | Dec-2021 |
Publisher: | Elsevier |
Abstract: | 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 $F^{p,\ell}_\alpha=H(\C)\cap L^p(\C,e^{-\frac{\alpha p}2|z|^{2\ell}})$. |
Note: | Reproducció del document publicat a: https://doi.org/10.1016/j.jmaa.2021.125481 |
It is part of: | Journal of Mathematical Analysis and Applications, 2021, vol. 504, p. 125481 |
URI: | http://hdl.handle.net/2445/184095 |
Related resource: | https://doi.org/10.1016/j.jmaa.2021.125481 |
ISSN: | 0022-247X |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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