Multifractal analysis of Hewitt-Stromberg measures with respect to gauge control functions

Abstract

This study provides a general multifractal formalism that overcomes the limitations of the traditional one. The generic Hewitt-Stromberg measures are used to introduce and study a multifractal formalism. The generic Hewitt-Stromberg dimensions' upper and lower bounds are estimated, producing results even at places $q$ where the upper and lower multifractal Hewitt-Stromberg dimension functions diverge.