We establish a weighted $L^p$ norm estimate for the Bergman projection for a class of pseudoconvex domains. We obtain an upper bound for the weighted $L^p$ norm when the domain is, for example, a bounded smooth strictly pseudoconvex domain, a pseudoconvex domain of finite type in ${\mathbb{C}}^2$, a convex domain of finite type in ${\mathbb{C}}^n$, or a decoupled domain of finite type in ${\mathbb{C}}^n$. The upper bound is related to the Bekollé-Bonami constant and is sharp. When the domain is smooth, bounded, and strictly pseudoconvex, we also obtain a lower bound for the weighted norm. As an additional application of the method of proof, we obtain the result that the Bergman projection is weak-type $(1,1)$ on these domains.

我们建立一个加权 ${\mathrm{大号}}^p$一类伪凸域的Bergman投影的范数估计。我们获得了加权的上限${\mathrm{大号}}^p$ 当域是例如有界的光滑严格伪凸域时的范数，该域是有限类型的伪凸域 ${\mathbb{C}}^{\mathrm{2个}}$，其中的有限类型的凸域 ${\mathbb{C}}^{ñ}$，或in中有限类型的解耦域 ${\mathbb{C}}^{ñ}$。上限与Bekollé-Bonami常数相关，并且很锐利。当该域是光滑的，有界的并且严格伪伪凸时，我们还获得了加权范数的下界。作为证明方法的另一项应用，我们获得了伯格曼投影为弱类型的结果$（\mathrm{1个}，\mathrm{1个}）$ 在这些域上。