A review on multifractal analysis of Hewitt-Stromberg measures

Abstract

We estimate the upper and lower bounds of the Hewitt$\text{-}$Stromberg dimensions. In particular, these results give new proofs of theorems on the multifractal formalism which is based on the Hewitt$\text{-}$Stromberg measures and yield results even at points $q$ for which the upper and lower multifractal Hewitt$\text{-}$Stromberg dimension functions differ. Finally, concrete examples of a measure satisfying the above property are developed.

To appear in Journal of Geometric Analysis

References in corpus (2)

• Coincidence and noncoincidence of dimensions in compact subsets of $[0,1]$
• On the projections of the multifractal Hewitt-Stromberg dimension functions

Cited by in corpus (1)

• On one map between singular expansions