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We obtain new bounds on the additive energy of (Ahlfors-David type) regularmeasures in both one and higher dimensions, which implies expansion results forsums and products of the associated regular sets, as well as more generalnonlinear functions of these sets. As a corollary of the higher-dimensionalresults we obtain some new cases of the fractal uncertainty principle in odddimensions.

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