论文标题
与Hölder相的振荡积分
On oscillatory integrals with Hölder phases
论文作者
论文摘要
我们展示了一个女性Hölder地图家族，尽管不是绝对连续的，但它满足了Van der Corput引理的分形版本。结果是Sahlsten和Steven Arxiv的最新作品的直接结果：2009.01703，该作品基于一种强大的波尔加因定理，称为sumproduct现象估计。我们使用Arxiv启发的基本方法给出了基本简单的证明：1704.02909，以检查应用总生产现象所需的非浓度估计值。这种方法使我们能够对衰减率进行额外的控制。
We exhibit a family of autosimilar Hölder maps that satisfies a fractal version of the Van Der Corput Lemma, despite not being absolutely continuous. The result is a direct consequence of a recent work of Sahlsten and Steven arXiv:2009.01703, which is based on a powerful theorem of Bourgain known as a sum-product phenomenon estimate. We give a substantially simpler proof of this fact in our particular context, using an elementary method inspired from arXiv:1704.02909 to check the non-concentration estimates that are needed to apply the sum-product phenomenon. This method allows us to gain additional control over the decay rate.
