We consider an inhomogeneous measure μ with the inhomogeneous part a self-similar measure ν, and show that for a given r ∈ (0,∞) the lower and the upper quantization dimensions of order r of μ are bounded below by the quantization dimension of ν and bounded above by a unique number , related to the temperature function of the thermodynamic formalism that arises in the multifractal analysis of μ.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba61-1-5,
author = {Mrinal Kanti Roychowdhury},
title = {Quantization Dimension Estimate of Inhomogeneous Self-Similar Measures},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {61},
year = {2013},
pages = {35-45},
zbl = {1264.28006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba61-1-5}
}
Mrinal Kanti Roychowdhury. Quantization Dimension Estimate of Inhomogeneous Self-Similar Measures. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 61 (2013) pp. 35-45. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba61-1-5/