某类柯西变换的一点注记

A Note about Certain Cauchy Transforms

假设{Sj}jq=-10是由压缩映射Sj(z)=εj+ρ(z-εj)(1.1)组成的迭代函数系(IFS),其中0<ρ<ρq(q4,ρq的定义见[1]),εj=e2πqji,K是{Sj}jq=-10的吸引子,μ是支撑在K上的Hausdorff测度.主要研究G(z)=∫K(1-zw)-1dμ(w)在其解析区域内的一些特殊的性质,得到G(n)(t)(0<t<1)界的某些估计.

Let the {Sj}q-1j=0 is an iterated function system （IFS） which consists of the compression mapping Sj（x）=εj＋ρ（x-εj）,0〈ρ〈ρq,q≥4,ρq is defined by [1], εj = e2xji/q K is the attractor of {Sj}q-1j=0,μ Hausdorff measure of surpport on k, this paper studies some special propersties of G（z） = ∫（1 - zw）-1 dμ（w） in its analytic region, some estimations of bound for G^（n）（t）（0 〈 t 〈 1） are obtained.