On one result of J. Bourgain

  • S. V. Konyagin Мат. ин-т РАН, Москва, Россия
  • I. D. Shkredov Моск. ун-т им. М. В. Ломоносова, Россия


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.
How to Cite
Konyagin, S. V., and I. D. Shkredov. “On One Result of J. Bourgain”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, no. 3, Mar. 2010, pp. 332–368, https://umj.imath.kiev.ua/index.php/umj/article/view/2872.
Research articles