Self-affine measures that are -improving
Kathryn E. Hare (2015)
Colloquium Mathematicae
Similarity:
A measure is called -improving if it acts by convolution as a bounded operator from 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 -improving if and only if they satisfy a suitable linear independence property. Certain self-affine measures are also seen to be -improving.