Self-affine measures that are $L^{p}$-improving

Kathryn E. Hare

Self-affine measures that are

L^{p}

-improving

Kathryn E. Hare

Colloquium Mathematicae, Tome 139 (2015), p. 229-243 / Harvested from The Polish Digital Mathematics Library

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Résumé

A measure is called $L^{p}$ -improving if it acts by convolution as a bounded operator from $L^{q}$ to L² for some q < 2. Interesting examples include Riesz product measures, Cantor measures and certain measures on curves. We show that equicontractive, self-similar measures are $L^{p}$ -improving if and only if they satisfy a suitable linear independence property. Certain self-affine measures are also seen to be $L^{p}$ -improving.

Publié le : 2015-01-01

Zbl 1315.28006

EUDML-ID : urn:eudml:doc:284351

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Kathryn E. Hare. Self-affine measures that are $L^{p}$-improving. Colloquium Mathematicae, Tome 139 (2015) pp. 229-243. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm139-2-5/