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arXiv · 1504.04893

$L^q$ dimensions and projections of random measures

Daniel Galicer·Santiago Saglietti·Pablo Shmerkin·Alexia Yavicoli
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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.

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Daniel Galicer, Santiago Saglietti, Pablo Shmerkin, Alexia Yavicoli. 2015-04-19. $L^q$ dimensions and projections of random measures. https://doi.org/10.1088/0951-7715%2F29%2F9%2F2609

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