Projections of mutual multifractal functions

Projections of measures with small supports

“…In [4,28], the authors studied the multifractal analysis of the orthogonal projections on m-dimensional linear subspaces of singular measures on R n satisfying the multifractal formalism. These results were later generalized by Selmi et al in [7,8,25,27,35,37].…”

“…In [8,9,30,36], the authors studied the mutual multifractal analysis of the orthogonal projections on m-dimensional linear subspaces. More specifically, they investigated the relationship between f µ,ν (α, β) and f µ V ,ν V (α, β), where…”

A generalization of O’Neil’s theorems for projections of measures and dimensions

“…Later on, Douzi and Selmi [13], considered the relative multifractal formalism developed by Cole [9], as they studied the relationship between the relative multifractal spectra of orthogonal projections of a measure µ in Euclidean space and those of µ. Recently, as a generalization of these results, Douzi and Selmi proved in [14,15] a relationship between the mutual multifractal spectra of a couple of measures (µ, ν) and its orthogonal projections in Euclidean spaces.…”