$L^q$ dimensions and projections of random measures
Dynamical Systems
2017-08-23 v1 Classical Analysis and ODEs
Abstract
We prove preservation of dimensions (for ) 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 -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 dimensions.
Keywords
Cite
@article{arxiv.1504.04893,
title = {$L^q$ dimensions and projections of random measures},
author = {Daniel Galicer and Santiago Saglietti and Pablo Shmerkin and Alexia Yavicoli},
journal= {arXiv preprint arXiv:1504.04893},
year = {2017}
}
Comments
30 pages, no figures