$L^q$ dimensions and projections of random measures

Abstract

We prove preservation of $L^q$ dimensions (for $1<q\le 2$) under all orthogonal projections for a class of random measures on the plane, which includes (deterministic) homogeneous self-similar measures and a well-known family of measures supported on $1$-variable fractals as special cases. We prove a similar result for certain convolutions, extending a result of Nazarov, Peres and Shmerkin. Recently many related results have been obtained for Hausdorff dimension, but much less is known for $L^q$ dimensions.

30 pages, no figures

References in corpus (1)

• Absolute continuity of self-similar measures, their projections and convolutions

Cited by in corpus (3)

• Absolute continuity of non-homogeneous self-similar measures
• Polynomial Fourier decay for fractal measures and their pushforwards
• Disintegration results for fractal measures and applications to Diophantine approximation