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arXiv · 2005.06365

The pyramid operator

A. Martina Neuman
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Abstract

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.

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A. Martina Neuman. 2020-05-13. The pyramid operator. https://arxiv.org/abs/2005.06365

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