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A differentiation theorem for uniform measures
Marc Carnovale
Using the notion of higher-order Fourier dimension introduced in \cite{M2} (which was a sort of psuedorandomness condition stemming from the Gowers norms of Additive Combinatorics)…
Long progressions in sets of fractional dimension
Marc Carnovale
We demonstrate -term arithmetic progressions in certain subsets of the real line whose "higher-order Fourier dimension" is sufficiently close to 1. This Fourier dimension, int…
Higher-order Fourier dimension and frequency decompositions
Marc Carnovale
This paper continues work begun in \cite{M1}, in which we introduced a theory of Gowers uniformity norms for singular measures on . There, given a -dimensional mea…
Gowers norms for singular measures
Marc Carnovale
Gowers introduced the notion of uniformity norm of a bounded function on an abelian group in order to provide a Fourier-theoretic pr…