L q dimensions and projections of random measures

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 familyof measures supported on 1-variable fractals as special cases. We prove asimilar result for certain convolutions, extending a result of Nazarov, Peresand Shmerkin. Recently many related results have been obtained for Hausdorffdimension, but much less is known for L q dimensions.