We obtain \(L^{p}\) bounds for the Bergman projection \(P_{\varphi }\) on \(\mathbb {C}^{n}\) for a class of weights \(\varphi \) whose complex Hessian has comparable eigenvalues. This relies on an extension of the estimate on the Bergman kernel obtained previously by Dall’Ara.

中文翻译：

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广义福克空间上伯格曼投影的 $$L^{p}$$ 估计

对于一类权重\(\varphi \ )，我们获得\ (\mathbb {C}^{n} \)上伯格曼投影\(P_{\varphi }\ ) 的 \ (L^{p}\)边界其复数 Hessian 矩阵具有可比较的特征值。这依赖于 Dall'Ara 先前获得的 Bergman 核估计的扩展。