Microlocal approach to the Hausdorff dimension of measures
Analysis of PDEs
2020-04-16 v2 Complex Variables
Abstract
In this paper we study the dependence of geometric properties of Radon measures, such as Hausdorff dimension and rectifiability of singular sets, on the wavefront set. This is achieved by adapting the method of Brummelhuis to the non-analytic case. As an application we obtain a general form of uncertainty principle for measures on the complex sphere which subsumes certain classical results about pluriharmonic measures.
Cite
@article{arxiv.2004.01626,
title = {Microlocal approach to the Hausdorff dimension of measures},
author = {Rami Ayoush and Michał Wojciechowski},
journal= {arXiv preprint arXiv:2004.01626},
year = {2020}
}
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