2017
Том 69
№ 6

# On one result of J. Bourgain

Abstract

In a linear space of dimension $n$ over the field $\mathbb{F}_2$, we construct a set $A$ of given density such that the Fourier transform of $A$ is large on a large set, and the intersection of $A$ with any subspace of small dimension is small. The results obtained show, in a certain sense, the sharpness of one theorem of J. Bourgain.

English version (Springer): Ukrainian Mathematical Journal 62 (2010), no. 3, pp 380-419.

Citation Example: Konyagin S. V., Shkredov I. D. On one result of J. Bourgain // Ukr. Mat. Zh. - 2010. - 62, № 3. - pp. 332–368.

Full text