The L^P-spaces of functions from the n-dimensional real space to the N-dimensional quaternionic space
Hamiltonian skew field of quaternions
Quaternion N-vectors
Quaternion-valued functions
L^p (R^n
H^N ) spaces
L^∞ (R^n
H^N ) space
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.
