Sharp superlevel set estimates for small cap decouplings of the parabola

• Yuqiu Fu ^[1] ; Larry Guth ^[1] ; Dominique Maldague ^[1]
  1. [1] Massachusetts Institute of Technology

     Massachusetts Institute of Technology

     City of Cambridge, Estados Unidos

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 39, Nº 3, 2023, págs. 975-1004
• Idioma: inglés
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• Resumen

  • We prove sharp bounds for the size of superlevel sets ¹x2R2 W jf .x/j>˛º, where ˛ > 0 and f W R2 ! C is a Schwartz function with Fourier transform supported in an R1 -neighborhood of the truncated parabola P 1 . These estimates imply the small cap decoupling theorem for P 1 of Demeter, Guth, and Wang (2020) and the canonical decoupling theorem for P 1 of Bourgain and Demeter (2015). New .`q ; Lp/ small cap decoupling inequalities also follow from our sharp level set estimates