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Self-affine measures that are L p -improving

Kathryn E. Hare (2015)

Colloquium Mathematicae

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.

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