JournalsrmiVol. 30, No. 4pp. 1281–1300

Discrete Fourier restriction associated with Schrödinger equations

  • Yi Hu

    Georgia Southern University, Statesboro, USA
  • Xiaochun Li

    University of Illinois at Urbana-Champaign, USA
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Abstract

We present a novel proof on the discrete Fourier restriction. The proof recovers Bourgain's level set result for Strichartz estimates associated with Schrödinger equations on a torus. Some sharp estimates on L2(d+2)/dL^{{2(d+2)}/{d}} norms of certain exponential sums in higher dimensional cases are established. As an application, we show that some discrete multilinear maximal functions are bounded on L2(Z)L^2(\mathbb Z).

Cite this article

Yi Hu, Xiaochun Li, Discrete Fourier restriction associated with Schrödinger equations. Rev. Mat. Iberoam. 30 (2014), no. 4, pp. 1281–1300

DOI 10.4171/RMI/815