Singular integrals along lacunary directions in Rn
Singular integrals along lacunary directions in Rn
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DOI：
10.1016/j.aim.2021.107580
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发表时间：
2019-07
影响因子：
1.7
通讯作者：
Natalia Accomazzo;F. Plinio;I. Parissis
中科院分区：
文献类型：
--
作者：
Natalia Accomazzo;F. Plinio;I. Parissis
Parcet和Rogers最近的一个结果是，有限阶空隙性表征了与R n中的无限方向集相关的最大平均算子的有界性。他们的证明是基于二维楔形体对脂肪超平面的几何组合覆盖。内格尔-斯坦-瓦格的种子结果依赖于n维性质的几何覆盖。本文给出了有限阶缺集的有限子集上奇异积分沿着的强势估计。以前的结果只涵盖了二维和三维的方向希尔伯特变换的特殊情况。证明是新的在所有方面和依赖，除其他想法外，在一个精确的覆盖n维Nagel-Stein-Wainger锥的二维Parcet-Rogers楔。
A recent result by Parcet and Rogers is that finite order lacunarity characterizes the boundedness of the maximal averaging operator associated to an infinite set of directions in R n. Their proof is based on geometric-combinatorial coverings of fat hyperplanes by two-dimensional wedges. Seminal results by Nagel-Stein-Wainger relied on geometric coverings of n-dimensional nature. In this article we find the sharp cardinality estimate for singular integrals along finite subsets of finite order lacunary sets in all dimensions. Previous results only covered the special case of the directional Hilbert transform in dimensions two and three. The proof is new in all dimensions and relies, among other ideas, on a precise covering of the n-dimensional Nagel-Stein-Wainger cone by two-dimensional Parcet-Rogers wedges.