Computational Methods and Function Theory 5 (2005), No. 2, 301--322
Copyright Heldermann Verlag 2005
Vladimir V. Andrievskii
andriyev@math.kent.edu , Department of Mathematical Sciences, Kent State University, Kent, OH 44242, U.S.A.
Let $E$ be a regular compact subset of the real line, let $g_{\overline{\mathbb{C}}\setminus E}(z,\infty)$ be the Green function of the complement of $E$ with respect to the extended complex plane $\overline{\mathbb{C}}$ with pole at $\infty$. We construct two examples of sets $E$ of the minimum Hausdorff dimension with $g_{\overline{\mathbb{C}}\setminus E}$ satisfying the H\"older condition with $p=1/2$ either uniformly or locally.
Keywords: Green's function, compact set, Hausdorff dimension, conformal invariants.
MSC 2000: Primary 30C10, 30C15, 41A10.
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