Analytic Properties of the Conformal Dirac Operator on the Sphere in Clifford Analysis

TL;DR

This paper explores the conformal Dirac operator on the sphere within Clifford analysis, establishing its properties and related Sobolev embeddings for Clifford algebra-valued functions.

Contribution

It introduces the conformal Dirac operator on the sphere and derives Sobolev embedding theorems for Clifford algebra-valued functions.

Findings

Defined the conformal Dirac operator on the sphere

Established Sobolev embedding theorems for Clifford functions

Analyzed the spinorial Laplacian of order d>0

Abstract

In this paper the conformal Dirac operator on the sphere is defined to be operating on the space of square-integrable Clifford algebra-valued functions. The spinorial Laplacian of order d>0 is defined and used to establish Sobolev embedding theorems.