Asian Journal of Mathematics

Volume 9 (2005)

Number 4

Some Exceptional Phenomena in Multifractal Formalism: Part II

Pages: 473 – 488

DOI: http://dx.doi.org/10.4310/AJM.2005.v9.n4.a2

Authors

De-Jun Feng

Ka-Sing Lau

Ka-Sing Lau

Xiang-Yang Wang

Xiang-Yang Wang

Abstract

In Part I we showed that the $L^q$-spectrum of the 3-fold convolution of the Cantor measure has a non-differentiable point at a $q_0 < 0$ [LW], therefore the standard multifractal formalism does not hold. In this Part II, we prove a modified multifractal formalism for the measure.

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