Bergman空间中函数与满足某种特定增长条件的解析函数的等价性的证明补充及推广  

Supplement and Generalization of the Proof of the Equivalence of Functions in Bergman Spaces with Analytic Functions Satisfying Certain Growth Conditions

作　　者：杨纪龙 孙铭浩 邴迪 

机构地区：[1]辽宁师范大学数学学院,辽宁 大连

出　　处：《理论数学》2024年第4期190-196,共7页Pure Mathematics

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。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 .

关 键 词：BERGMAN空间 解析函数类 增长条件 

分 类 号：O17[理学—数学]