Resumen de Sharp superlevel set estimates for small cap decouplings of the parabola

Yuqiu Fu, Larry Guth, Dominique Maldague

• 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