Abstract
The vector-valued measure generated by the self-conformal iterated function system (IFS) was introduced by the author (2004 J. Math. Anal. Appl. 299 341–56). Its variation is scalar measure. This paper proves that the Lq-spectrum of the variation measure is differentiable and the corresponding multifractal formalism holds, if the relevant IFS satisfies the open set condition. This result can be applied to the study of self-conformal (scalar) measures generated by certain IFS with overlaps.
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