Let S-j(z) = epsilon(j) + (z- epsilon(j))/2 be an iterated function system, where epsilon(j) = e(2j pi i/3) for j = 0, 1, 2. Then, there exists a uniform self-similar measure mu supported on a compact set K, which is the attractor of {S (j)}(j=0)(2). The Hausdorff dimension of the attractor K is alpha = log 3/ log 2. Let F(z) =integral K(z - omega)(-1)d mu(omega) be the Cauchy transform of mu. In this paper, we consider the Hardy space and the multiplier property of F. We prove that F ' belongs to Hp for 0 < p < 1/(2 - alpha)...
