ACTA issues

The relative multifractal analysis, review and examples

Bilel Selmi

Acta Sci. Math. (Szeged) 86:3-4(2020), 635-666

Abstract. In the present paper, we suggest new proofs of many known results about the {\it relative multifractal formalism}. We provide results even at points $q$ for which the relative multifractal Hausdorff and packing functions differ. We also give some examples of two measures where the multifractal functions are different and the Hausdorff dimension of the level sets of the $\nu $-local Hölder exponent is given by the Legendre transform of the multifractal Hausdorff function and their packing dimension by the Legendre transform of the multifractal packing function.

DOI: 10.14232/actasm-020-801-8

AMS Subject Classification (1991): 28A78, 28A80

Keyword(s): relative multifractal analysis, multifractal formalism, multifractal Hausdorff measure, multifractal packing measure, Hausdorff dimension, packing dimension, Moran measures

received 1.5.2020, revised 10.9.2020, accepted 21.9.2020. (Registered under 51/2020.)