A sparse domination principle for rough singular integrals
A sparse domination principle for rough singular integrals
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DOI：
10.2140/apde.2017.10.1255
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发表时间：
2016-12
期刊：
影响因子：
2.2
通讯作者：
José M. Conde-Alonso;Amalia Culiuc;F. Plinio;Yumeng Ou
中科院分区：
文献类型：
--
作者：
José M. Conde-Alonso;Amalia Culiuc;F. Plinio;Yumeng Ou
我们证明了与$\mathbb R^d$上的粗糙齐次奇异积分$T_\Omega$（其中L^q（S^{d-1}）中的角部分$\Omega \具有消失平均值且$1<q\leq \infty$）以及与$\mathbb R^d$中的Bochner-Riesz平均值在临界指数处相关联的双线性形式由包含$（1，p）$平均值的稀疏形式所支配。这种支配比T_\Omega$和Bochner-Riesz平均值的弱L^1估计更强，分别是由于Seeger和Christ。此外，我们的控制定理作为推论，对Bochner-Riesz平均和具有无界角部分的齐次奇异积分给出了新的精确的A_p加权估计，推广了Hytonen-Roncal-Tapiola关于T_Omega的结果.我们的研究结果遵循一个新的抽象稀疏支配原则，不依赖于弱端点估计的最大截断。
We prove that bilinear forms associated to the rough homogeneous singular integrals $T_\Omega$ on $\mathbb R^d$, where the angular part $\Omega \in L^q (S^{d-1})$ has vanishing average and $1<q\leq \infty$, and to Bochner-Riesz means at the critical index in $\mathbb R^d$ are dominated by sparse forms involving $(1,p)$ averages. This domination is stronger than the weak-$L^1$ estimates for $T_\Omega$ and for Bochner-Riesz means, respectively due to Seeger and Christ. Furthermore, our domination theorems entail as a corollary new sharp quantitative $A_p$-weighted estimates for Bochner-Riesz means and for homogeneous singular integrals with unbounded angular part, extending previous results of Hyt\"onen-Roncal-Tapiola for $T_\Omega$. Our results follow from a new abstract sparse domination principle which does not rely on weak endpoint estimates for maximal truncations.