We undertake a general study of multifractal phenomena for functions or measures. We show that the existence of several kinds of multifractal functions or measures can be easily deduced from an abstract statement, leading to new results. This general approach does not work for Fourier or Dirichlet series. Using careful constructions, we extend our results to these cases.
Cite this article
Frédéric Bayart, Yanick Heurteaux, Multifractal phenomena and packing dimension. Rev. Mat. Iberoam. 35 (2019), no. 3, pp. 767–804DOI 10.4171/RMI/1069