Additive energy of regular measures in one and higher dimensions, and the fractal uncertainty principle

Abstract

We obtain new bounds on the additive energy of (Ahlfors-David type) regular measures in both one and higher dimensions, which implies expansion results for sums and products of the associated regular sets, as well as more general nonlinear functions of these sets. As a corollary of the higher-dimensional results we obtain some new cases of the fractal uncertainty principle in odd dimensions.

arXiv comment38 pages, 5 figures. This is the publication version, incorporating the journal style

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Cited by in corpus (1)

• Fractal uncertainty principle for discrete Cantor sets with random alphabets