摘要: 本文分两个部分对属于某个Bergman空间
的解析函数类与满足某种特定增长条件的解析函数的等价性的证明进行补充。首先通过两个引理以及Hölder不等式来证明对于
，有
，此时只要求函数
解析即可，而文献中却要求
，因此是文献中叙述的进一步推广。其次，利用贝塔函数的积分形式，便能够得到若
时，
以及
时，同样有
。
Abstract:
This paper is divided into two parts to supplement the proof of equivalence between the class of analytic functions belonging to a certain Bergman space
and the analytic functions satisfying certain growth conditions. First of all, two lemmas and the Hölder inequality are used to prove that for
, there is
. At this time, only the function
is required to be analyzed, while
is required in literature, so it is a further generalization of what is described in literature. Secondly, using the integral form of the beta function, we can find that if
,
, and
, also
.