Some Properties of a Cauchy Transform on Sierpinski Carpet

Let
$z2j=e^{\frac{2j+1}{4}}, z_{2j+1} =\frac{\sqrt{2}}{2}e^{\frac{2j}{4}\pi i},\ j=0,1,2,3$
, and let
$S_{jz}= \frac{1}{3}(z-z)+z, j=0,1, \cdots, 7$
. Let
$K$
be the attractor of
$\{S_{j}\}_{j=0}^{7},\mathrm{K}$
is called Sierpinski Carpet, and
$\mu$
be regularizing Hausdorff measure of support on
$K, P(z)=j_{K}(z-w)^{-1}d\mu(w)$
be the Cauchy transform of
$\mu$
. we can see that
$P(z)$
is analytic in
$\vert z\vert > 1$
, and derive Some properties of
$P(z)$
.