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

• Autorzy: Kathryn E. Hare
• Języki publikacji: EN

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.

Kategorie tematyczne

• 42A38: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
• 43A05: Measures on groups and semigroups, etc.
• 28A80: Fractals

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2015
• Tom: 139
• Numer: 2
• Strony: 229-243

Daty

wydano

2015

Twórcy

autor

Kathryn E. Hare

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

Identyfikatory

DOI

10.4064/cm139-2-5