在1991年柯倫布朗猜測會存在一個常數c屬於(0,1)，使得對於任意解析函數f(z)和g(z)滿足“在環帶A(c,1)上，f(z)的絕對值小於或等於g(z)的絕對值”，則f的柏格曼範數會小於或等於g的柏格曼範數。
本篇文章中主要是在加權柏格曼空間上考慮柯倫布朗猜想，並給出幾個柯倫布朗猜想在加權柏格曼空間上的部分結果。

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