论文标题
抛物线的分形子集的脱钩
Decoupling for fractal subsets of the parabola
论文作者
论文摘要
我们考虑将抛物线的分形子集解耦。我们减少了研究$ l^{2} l^{p} $解耦合在抛物线子$ \ {（t，t，t^2）上的分形子集：0 \ leq t \ leq 1 \} $，用于研究$ l^{2} l^{2} l^{p/3} $ decoupling for this sukeption of this sukeption $ netters $ netters $ nikeption $ nikeption $ nikeption $ nikeption $ nikeption $ nikeption $ nikeption $ nikeptive。这概括了在抛物线的情况下，波尔加因仪的解耦定理。由于稀疏性和类似的结构，这使我们可以在抛物线的抛物线的demoter脱钩定理时改善。在$ p/3 $是一个甚至整数的情况下，我们会得出理论和计算工具，以明确计算该预测的相关解耦常数为$ [0，1] $。我们的想法灵感来自Biggs使用嵌套有效的一致性的最新工作。
We consider decoupling for a fractal subset of the parabola. We reduce studying $l^{2}L^{p}$ decoupling for a fractal subset on the parabola $\{(t, t^2) : 0 \leq t \leq 1\}$ to studying $l^{2}L^{p/3}$ 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.
