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Colloquium Mathematicum

2015 | 139 | 2 | 229-243

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

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Abstrakty

EN
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.

229-243

wydano
2015

Twórcy

autor
• Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1