JournalsrmiVol. 37, No. 5pp. 1761–1802

An l2l^2 decoupling interpretation of efficient congruencing: the parabola

  • Zane Kun Li

    Indiana University, Bloomington, USA
An $l^2$ decoupling interpretation of efficient congruencing: the parabola cover
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Abstract

We give a new proof of l2l^2 decoupling for the parabola inspired from efficient congruencing. Making quantitative this proof matches a bound obtained by Bourgain for the discrete restriction problem for the parabola. We illustrate similarities and differences between this new proof and efficient congruencing and the proof of decoupling by Bourgain and Demeter. We also show where tools from decoupling such as l2L2l^2L^2 decoupling, Bernstein’s inequality, and ball inflation come into play.

Cite this article

Zane Kun Li, An l2l^2 decoupling interpretation of efficient congruencing: the parabola. Rev. Mat. Iberoam. 37 (2021), no. 5, pp. 1761–1802

DOI 10.4171/RMI/1248