Self-affine multifractal Sierpiński sponges in \(\mathbb{R}^d\) (Q1392500)

The author uses a multifractal formalism introduced in an earlier paper (based on variants of Hausdorff and packing measure with some additional weights) to prove new multifractal phenomena for self-affine multifractals (self-affine Sierpiński sponge) in \(\mathbb{R}^d\) that do not occur in the self-similar setting. He assumes a strong separation condition to find, for example, the Hausdorff spectrum or the multifractal dimension functions, which he introduced previously, but he conjectures that this condition can be omitted. One new phenomenon, in sharp contrast to the self-similar settting, is that the dimension functions for generalized multifractal Hausdorff and packing dimensions do not coincide.