Abstract
In 1991, Korenblum presented his conjecture on Bergman spaces. He speculated that if $f(z)$ and $g(z)$ are two holomorphic functions on the unit disc in the complex plane, then there exists a number $0<c<1$ such that the condition "$|f(z)|\geq|g(z)|$" could implies "$||f||_{2}\geq||g||_{2}$", where $||.||_{2}$ is the Bergman norm. This maximum principle was confirmed in 1999 by Hayman. It is not only an analogous property with $H^{p}$ spaces but also inspires numerous research in other function spaces. In this article we introduce the development of this problem and the related research results from which the idea originally came from Korenblum's maximum principle. In the end we give some discussions about the circumstances when the functions are constrained in the form of $\prod(z-a_{i})$ for $ -1 \leq a_{i} \leq 1$.