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The aim of this paper is to study the behavior of the multifractal Hewitt-Stromberg dimension functions under projections in Euclidean space. As an application, we study the multifractal analysis of the projections of a measure. In particular, we obtain general results for the multifractal analysis of the orthogonal projections on $m$-dimensional linear subspaces of a measure $\mu$ satisfying the multifractal formalism which is based on the Hewitt-Stromberg measures., Comment: arXiv admin note: Substantial text overlap with arXiv:1901.03834. Text overlap with arXiv:1711.05316 by other authors

In this paper, we are concerned both with the properties of the generalization of the L^q-spectrum relatively to two Borel probability measures and with the generalized q-dimension Riesz capacity. We are also interested in the study of their behaviors under orthogonal projections.

The aim of this article is to study the behaviour of the relative multifractal spectrum under projections. First of all, we depict a relationship between the mutual multifractal spectra of a couple of measures $(\mu, \nu)$ and its orthogonal projections in Euclidean space. As an application, we improve Svetova's result (Tr. Petrozavodsk. Gos. Univ. Ser. Mat., 11 (2004), 41-46) and study the mutual multifractal analysis of the projections of measures.

In this paper, we are concerned with the properties of the generalization of the L q-spectrum relatively to two Borel probability measures having the same compact support and we are interested in the generalized of q-dimension Riesz capacity and also in the study of their behaviors under orthogonal projections., Dans cette article, on s'intéresse en premier lieu par les propriétés de la généralisation du L q-spectre relativement a deux mesures de probabilité de Borel ayant le même support compact. En deuxième lieu on s'intéresse par la q-dimension de la capacité de Riesz généralisée dans l'étude du comportement des sous projections orthogonales.