Clifford Analysis on Orlicz-Sobolev Spaces

TL;DR

This paper extends Clifford analysis to Orlicz-Sobolev spaces, exploring the properties of the Dirac operator and Teodorescu transform, and establishing decomposition results for Clifford-valued Orlicz spaces.

Contribution

It introduces the theoretical framework of Clifford analysis within Orlicz-Sobolev spaces, including mapping properties and space decompositions, which are novel contributions.

Findings

Mapping properties of Dirac operator and Teodorescu transform established

Decomposition results for Clifford valued Orlicz spaces derived

Analogous theoretical results of Clifford analysis extended to Orlicz-Sobolev spaces

Abstract

In this article we develop few of the analogous theoretical results of Clifford analysis over Orlicz-Sobolev spaces and study mapping properties of the Dirac operator and the Teodorescu transform over these function spaces. We also get analogous decomposition results of Clifford valued Orlicz spaces and the generalized Orlicz-Sobolev spaces.