We establish an embedding theorem for the weighted Bergman spaces induced by a positive Borel measure \(d\omega (y)dx\) with the doubling property \(\omega (0,2t)\le C\omega (0,t)\). The characterization is given in terms of Carleson squares on the upper half-plane. As special cases, our result covers the standard weights and logarithmic weights. As an application, we also establish the boundedness of the area operator.

中文翻译：

---

倍增测度在Bergman空间上的嵌入定理和区域算子

我们为具有正则Borel测度\（d \ omega（y）dx \）并具有加倍属性\（\ omega（0,2t）\ le C \ omega（0，t）的加权Bergman空间建立一个嵌入定理\）。根据上半平面上的Carleson平方给出特征。作为特殊情况，我们的结果包括标准权重和对数权重。作为应用程序，我们还建立了区域运算符的有界性。