Sharp superlevel set estimates for small cap decouplings of the parabola
Yuqiu Fu
Massachusetts Institute of Technology, Cambridge, USALarry Guth
Massachusetts Institute of Technology, Cambridge, USADominique Maldague
Massachusetts Institute of Technology, Cambridge, USA
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Abstract
We prove sharp bounds for the size of superlevel sets , where and is a Schwartz function with Fourier transform supported in an -neighborhood of the truncated parabola . These estimates imply the small cap decoupling theorem for of Demeter, Guth, and Wang (2020) and the canonical decoupling theorem for of Bourgain and Demeter (2015). New small cap decoupling inequalities also follow from our sharp level set estimates.
Cite this article
Yuqiu Fu, Larry Guth, Dominique Maldague, Sharp superlevel set estimates for small cap decouplings of the parabola. Rev. Mat. Iberoam. 39 (2023), no. 3, pp. 975–1004
DOI 10.4171/RMI/1393