We define a class of measures having the following properties: (1) the measures are supported on self-similar fractal subsets of the unit cube , with 0 and 1 identified as necessary; (2) the measures are singular with respect to normalized Lebesgue measure m on ; (3) the measures have the convolution property that for some ε = ε(p) > 0 and all p ∈ (1,∞). We will show that if (1/p,1/q) lies in the triangle with vertices (0,0), (1,1) and (1/2,1/3), then for any measure μ in our class.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm109-2-1,
author = {Denise Szecsei},
title = {A convolution property of some measures with self-similar fractal support},
journal = {Colloquium Mathematicae},
volume = {107},
year = {2007},
pages = {171-177},
zbl = {1118.43001},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm109-2-1}
}
Denise Szecsei. A convolution property of some measures with self-similar fractal support. Colloquium Mathematicae, Tome 107 (2007) pp. 171-177. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm109-2-1/