The pyramid operator

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.

References in corpus (1)

• $L^2\times L^2\times L^2\to L^{2/3}$ boundedness for trilinear multiplier operator