The n-dimensional generalized Hartogs triangles are domains defined by ${\mathbb{H}}_{\mathbf{p}}^n:=\left\{\right(z_1,\dots ,z_n)\in {\mathbb{C}}^n:|z_1{|}^{p_1}<\cdots <|z_n{|}^{p_n}<1\}$ with $\mathbf{p}:=(p_1,\dots ,p_n)\in ({\mathbb{Z}}^{+}{)}^n$ and $n\ge 2$. In this paper, we first obtain an estimate for the Bergman kernel of ${\mathbb{H}}_{\mathbf{p}}^n$ and then use it to establish the $L^p$ boundedness of the associated Bergman projections. Our result generalizes the $L^p$ boundedness result for two-dimensional generalized Hartogs triangles obtained by L.D. Edholm and J.D. McNeal in [Bergman subspaces and subkernels: degenerate Lp mapping and zeroes. J Geom Anal. 2017;27:2658–2683] to n-dimensional settings.

所述Ñ维超Cartan广义三角形结构域由下式定义${\mathbb{H}}_{\mathbf{磷}}^n:=\left\{\right(z_1,\dots ,z_n)\in {\mathbb{C}}^n：|z_1{|}^{{磷}_1}<\cdots <|z_n{|}^{{磷}_n}<1\}$ 和 $\mathbf{磷}:=({磷}_1,\dots ,{磷}_n)\in ({\mathbb{Z}}^{+}{)}^n$ 和 $n\ge 2$. 在本文中，我们首先获得了对 Bergman 核的估计${\mathbb{H}}_{\mathbf{磷}}^n$ 然后用它来建立 ${升}^{磷}$相关的 Bergman 投影的有界性。我们的结果概括了${升}^{磷}$LD Edholm 和 JD McNeal 在 [Bergman subspaces and subkernels: degenerate Lp mapping and zeroes. 中获得的二维广义 Hartogs 三角形的有界结果。J Geom 肛门。2017;27:2658-2683] 到n维设置。