Geodesic
Self-affine measures that are $L^{p}$-improving
Kathryn E. Hare1
1 Department of Pure Mathematics University of Waterloo Waterloo, Ontario, Canada N2L 3G1
Colloquium Mathematicum, Tome 139 (2015) no. 2, pp. 229-243

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

A measure is called $L^{p}$-improving if it acts by convolution as a bounded operator from $L^{q}$ to $L^{2}$ for some $q2$. 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.
DOI : 10.4064/cm139-2-5
Keywords: measure called improving acts convolution bounded operator interesting examples include riesz product measures cantor measures certain measures curves equicontractive self similar measures improving only satisfy suitable linear independence property certain self affine measures seen improving

Kathryn E. Hare 1

1 Department of Pure Mathematics University of Waterloo Waterloo, Ontario, Canada N2L 3G1 
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Kathryn E. Hare. Self-affine measures that are $L^{p}$-improving. Colloquium Mathematicum, Tome 139 (2015) no. 2, pp. 229-243. doi: 10.4064/cm139-2-5

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