Multifractal analysis of a class of self-affine Moran sets

Abstract

In the paper, we investigate the fine multifractal spectrum of a class of self-affine Moran sets with fixed frequencies, and we prove that under certain separation conditions, the fine multifractal spectrum $H(\alpha )$ is given by the formula $$H(\alpha )=\underset{-\infty <t<+\infty }{\inf }\{\alpha t+\beta (t)\}.$$