On the Properties of the Pre-Schwarz Norm of Functions in the Class SL<sup>*</sup>

前施瓦茨范数作为复分析研究中的重要工具，在研究复映射的几何性质、单叶性准则及Teich-mller空间理论等方面发挥关键作用。本文研究在单位圆盘上满足从属关系的标准化解析单叶函数类SL∗的前施瓦茨范数估计问题。本文首先系统梳理了相关研究进展，然后基于施瓦茨函数的性质及其相关推广形式，结合多元函数极值理论，得到了SL∗类函数前施瓦茨范数的上界估计。The pre-Schwarz norm, as an important tool in complex analysis, plays a crucial role in studying the geometric properties of complex mappings, criteria for univalence, and the theory of Teichmüller spaces. This paper investigates the estimation of the pre-Schwarz norm for the class of normalized analytic univalent functions SL∗ that satisfy subordination relations on the unit disk. The paper first systematically reviews the related research progress, and then, based on the properties of Schwarz functions and their related generalizations, and combining multivariable extremal function theory, derives an upper bound estimate for the pre-Schwarz norm of functions in the class SL∗.