Lipschitz曲线上Cauchy积分有界性的注记（$p=2$）
Notes of Boundedness on Cauchy Integrals on Lipschitz Curves ($p=2$)
摘要：
给出了\cite{CJS89}中第一个证明的细节，证明了Lipschitz曲线上$L^2$ ~函数的柯西变换是有界的.证明了Lipschitz曲线上的$L^2$ ~-函数是Lipschitz曲线上和Lipschitz曲线下域上的Hardy空间$H^2(Ω_\pm)$中函数的非切边界极限之和.在以Lipschitz曲线为实轴的条件下，得到了Cauchy变换的一个更精确的边界。
英文摘要：
We provide the details of the first proof in~\cite{CJS89}, which proved that Cauchy transform of $L^2$~functions on Lipschitz curves is bounded. We then prove that every $L^2$~function on Lipschitz curves is the sum of non-tangential boundary limit of functions in $H^2(Ω_\pm)$, the Hardy spaces on domains over and under the Lipschitz curve. We also obtain a more accurate boundary of Cauchy transform under the condition that the Lipschitz curve is the real axis.
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