Singular Integrals associated with Reflection Groups on Euclidean Space

TL;DR

This paper extends harmonic analysis by studying singular integrals influenced by reflection groups on Euclidean space and establishes a T1 theorem for these integrals.

Contribution

It introduces a new class of singular integrals associated with reflection groups and proves a T1 theorem for their boundedness.

Findings

Established the T1 theorem for reflection group-related singular integrals

Extended harmonic analysis techniques to include reflection symmetries

Provided foundational results for further study of geometric harmonic analysis

Abstract

In the field of harmonic analysis, geometric considerations are frequently crucial. Specially, group actions such as translations, dilations and rotations on Euclidean space are instrumental. The objective of this paper is to extend the study of singular integrals to include the effects of group reflections on Euclidean space, and to establish the T1 theorem for these singular integrals.