Abstract

We prove preservation of L-q dimensions (for 1 q = 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.