Concerning Integrals of Moduli of Regular Functions along Convex Curves
Concerning Integrals of Moduli of Regular Functions along Convex Curves
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关于正则函数模沿凸曲线的积分
DOI：
10.1112/plms/s2-39.1.216
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发表时间：
1935
期刊：
影响因子：
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通讯作者：
R. Gabriel
中科院分区：
文献类型：
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作者：
R. Gabriel
在那之后不久，我证明了定理的特例，其中外曲线F是圆，通过涉及逆和反射思想的论点，与F的特殊性质密不可分地联系在一起，在这个特例中我得到了。4=2.我现在给出一个证明上述一般定理的论证；然而，它不能证明A=2。在本文的最后一节，我还得到了类似于定理I的结果，其中放宽了F的凸性条件。该方法包括将F的内部变换到
Shortly after that time I proved* the special case of the theorem in which the outer curve F is a circle, by means of arguments involving ideas of inversion and reflection, inextricably associated with the special nature of F, and in this special case I obtained. 4= 2. I now give an argument which proves the general theorem as stated above; it does not, however, yield A= 2. I also obtain in the final section of this paper a result analogous to Theorem I in which the condition of the convexity of F is relaxed. The method consists of transforming the interior of F on to the