Affiliation:
1. Friedrich-Schiller Universität Jena, Mathematisches Institut, Ernst-Abbe-Platz 1–4, D-07743 Jena, Germany
Abstract
Abstract
In this note we shall consider the following problem: which conditions should satisfy a function ℎ : (0, 1) → ℝ in order to guarantee the existence of a (regular) measure μ in with compact support and
for some positive constants 𝑐2, and 𝑐2 independent of γ ∈ Γ and 𝑟 ∈ (0,1)? The theory of self-similar fractals provides outstanding examples of sets fulfilling (♡) with ℎ(𝑟) = 𝑟𝑑, 0 ≤ 𝑑 ≤ 𝑛, and a suitable measure μ. Analogously, we shall rely on some recent techniques for the construction of pseudo self-similar fractals in order to deal with our more general task.
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