The L^P-spaces of functions from the n-dimensional real space to the N-dimensional quaternionic space

Hussien A. H. Abugirda; Mohammed Kh. Abdullah; Khaldoun S. Al-Yasiri

doi:10.24996/ijs.2024.65.1.21

Authors

Hussien A. H. Abugirda Department of Mathematics, College of Science, University of Basrah, Basrah, Iraq https://orcid.org/0000-0002-0565-8763
Mohammed Kh. Abdullah Department of Mathematics, College of Science, University of Basrah, Basrah, Iraq https://orcid.org/0000-0003-4879-1190
Khaldoun S. Al-Yasiri Department of Mathematics, College of Science, University of Basrah, Basrah, Iraq https://orcid.org/0000-0002-9625-5803

DOI:

https://doi.org/10.24996/ijs.2024.65.1.21

Keywords:

Hamiltonian skew field of quaternions, Quaternion N-vectors, Quaternion-valued functions, L^p (R^n,H^N ) spaces, L^∞ (R^n,H^N ) space

Abstract

In this paper, we introduce new definitions of the - spaces namely the - spaces Here, and are natural numbers that are not necessarily equal, such that . The space refers to the n-dimensional Euclidean space, refers to the quaternions set and refers to the N-dimensional quaternionic space. Furthermore, we establish and prove some properties of their elements. These elements are quaternion-valued N-vector functions defined on , and the spaces have never been introduced in this way before.