论文标题
金字塔操作员
The pyramid operator
论文作者
论文摘要
本文给出了在歧管$ m $上定义的积分运算符的概念，该操作员由$ \ mathbb {r}^{d} $组成的三重点组成，构成了带有原始的常规$ 3 $ -SIMPLEX。研究了此类操作员的界限。有限的区域包含的比Banach范围还要多 - 这一事实反映了球形$ l^{p} $ - 改进估计值。本文的目的是两个方面：一个是通过由高维常规简单创建的歧管研究成整体操作员，两个是为该积分运算符启动最大运算符理论。
This paper gives a concept of an integral operator defined on a manifold $M$ consisting of triple of points in $\mathbb{R}^{d}$ making up a regular $3$-simplex with the origin. The boundedness of such operator is investigated. The boundedness region contains more than the Banach range - a fact that mirrors the spherical $L^{p}$-improving estimate. The purpose of this paper is two-fold: one is to investigate into an integral operator over a manifold created from high-dimensional regular simplices, two is to start a maximal operator theory for such integral operator.
