一个Hausdorff测度的柯西变换的罗朗系数估计

假设{S_j})j~5=0是由压缩映射 S_j(z)=ε_j+1/3(z-ε),■=0,1,2,3,4,5．组成的迭代函数系(IFS),K 是{S_j}_j~5=0的吸引子,μ是支撑在 K 上的 Hausdorff 测度．最近,文1]中讨论了自相似测度的柯西变换 F 在|z|＞1内的罗朗系数．研究 g(z)：=F(1/3z)=(?)dμ(ω)在|z|＜1内的罗朗系数,得到了一些结果．

Estimations of Laurent Coefficients of A Cauchy Transforms of Hausdorff Measure

Let the iterated function system (IFS) {S_j}+j~5=0 is of the form S_j(z)=∈_j+(1/3)(z-∈_j),∈_j=(?),j=0,1,2,3,4,5. K is the attractor of {S_j}_j~5=0,μis Hausdorff measure of surpport on K.Recently,the paper1]have studied the Laurent coefficients of such transform F of Hausdorff measure in |z|＞1.In this paper,we mainly consider the Laurent coefficients of g(z):=F((1/3)z)= ∫_k((1/3)z-w)~(-1)dμ(w)in|z|＜1.We get some results.