Sierpinski垫上的Cauchy变换所涉及的一个辅助函数的一点注记

A Note of an Auxiliary Function Related to the Cauchy Transform on the Sierpinski Gasket

设Sierpinski垫上Hausdorff测度的Cauchy变换为F(z).考虑了一个与F(z)相关的辅助函数.得到了它在负实轴上具有保号性.此性质将对研究F(z)的一些有趣的分形性质有所帮助.

Let F（z） be the Cauchy transform of Hausdorff measure restricted on the Sierpinski gasket. An auxiliary function related to F（z） is considered. It is proved that the function preserves sign on negative real axis. The property will contribute to the study of some interested fractal properties of F （z）.