Papers › Decoupling for fractal subsets of the parabola
Decoupling for fractal subsets of the parabola
Alan Chang, Jaume de Dios Pont, Rachel Greenfeld, Asgar Jamneshan, Zane Kun Li, José Madrid
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We consider decoupling for a fractal subset of the parabola. We reduce studying l²Lᵖ decoupling for a fractal subset on the parabola {(t, t²) : 0 ≤t ≤1} to studying l²L^(p/3) decoupling for the projection of this subset to the interval [0, 1]. This generalizes the decoupling theorem of Bourgain-Demeter in the case of the parabola. Due to the sparsity and fractal like structure, this allows us to improve upon Bourgain-Demeter's decoupling theorem for the parabola. In the case when p/3 is an even integer we derive theoretical and computational tools to explicitly compute the associated decoupling constant for this projection to [0, 1]. Our ideas are inspired by the recent work on ellipsephic sets by Biggs using nested efficient congruencing.
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