Mixed multifractal dimensions of overlaps of self-similar sets and measures
Jihed Hattab
Source abstract
In recent times, the mixed multifractal analysis has generated interest. The purpose of this paper is twofold. Firstly, we define the mixed multifractal Hewitt-Stromberg measures and introduce a multifractal formalism based on this type of measures. Secondly, we prove that the upper mixed multifractal box-dimension of the overlaps of self-similar sets and measures is strictly smaller than the mixed multifractal Hausdorff dimension of selfsimilar sets and measures. Finally, we demonstrate that this result is still valid for the mixed multifractal Hewitt-Stromberg dimensions.
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