Bounds for the Lq-spectra of a self-similar multifractal not satisfying the Open Set Condition

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:355

Article

Olsen, L.

关键词: Multifractals;    Self-similar measure;    L-q-spectra;   

DOI  :  10.1016/j.jmaa.2009.01.037

来源: Elsevier

【 摘 要 】

By now the L-q-spectra of self-similar measures satisfying the so-called Open Set Condition is well understood. However, if the Open Set Condition is not satisfied, then almost nothing is known. In this paper we provide non-trivial bounds for the L-q-spectra of an arbitrary self-similar measure. We emphasize that we are considering arbitrary self-similar measures (and sets) which are not assumed to satisfy the Open Set Condition or similar separation conditions. (c) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free