We establish characterizations of the radial weights ω on the unit disc such that the Bergman projection $P_{\omega }$, induced by ω, is bounded and/or acts surjectively from $L^{\infty }$ to the Bloch space $\mathcal{B}$, or the dual of the weighted Bergman space $A_{\omega }^1$ is isomorphic to the Bloch space under the $A_{\omega }^2$-pairing. We also solve the problem posed by Dostanić in 2004 of describing the radial weights ω such that $P_{\omega }$ is bounded on the Lebesgue space $L_{\omega }^p$, under a weak regularity hypothesis on the weight involved. With regard to Littlewood-Paley estimates, we characterize the radial weights ω such that the norm of any function in $A_{\omega }^p$ is comparable to the norm in $L_{\omega }^p$ of its derivative times the distance from the boundary. This last-mentioned result solves another well-known problem on the area. All characterizations can be given in terms of doubling conditions on moments and/or tail integrals ${\int }_r^1\omega (t)dt$ of ω, and are therefore easy to interpret.

我们在单位圆盘上建立径向权重ω 的特征，使得伯格曼投影${磷}_{\omega }$，由ω诱导，有界和/或从${升}^{\infty }$ 到布洛赫空间 $\mathcal{乙}$，或加权伯格曼空间的对偶 ${一}_{\omega }^1$ 与 Bloch 空间同构 ${一}_{\omega }^2$-配对。我们还解决了 Dostanić 在 2004 年提出的描述径向权重ω 的问题，使得${磷}_{\omega }$ 在 Lebesgue 空间上有界 ${升}_{\omega }^{磷}$，在所涉及的权重的弱规律性假设下。关于 Littlewood-Paley 估计，我们刻画径向权重ω，使得任何函数的范数在${一}_{\omega }^{磷}$ 与标准中的标准相当 ${升}_{\omega }^{磷}$其导数乘以到边界的距离。最后提到的这个结果解决了该地区另一个众所周知的问题。所有特征都可以根据矩和/或尾积分的加倍条件给出${\int }_r^1\omega (吨)d吨$的ω，因此是很容易理解。