# RELATIONS BETWEEN TWO CLASSES OF FUNCTIONS

Document Type : Research Paper

Author

Department of Mathematics, University of hormozgan, Bandarabbas, Iran

10.22103/jmmrc.2021.14614.1100

Abstract

Let F denote a specific space of the class of was costructed by H. Khodabakhshian
as a classes of separable Banach function spaces analogous to the james function spaces. In this
notes we prove that l_p(α) is isomorphic to a complemented subspace of F_{α,p} and for p = 2, F_{α,p} is a closed subspace of the Waterman-Shiba space αBV^ (p)
Assume F denotes a specific space of the class of F_{α,p} that was costructed by H.
Khodabakhshian[2] as a classes of separable Banach function spaces analogous to the James
function spaces. In this notes we prove that l_p(α) is isomorphic to a complemented subspace of
F_{α,p} and for p = 2, F_{α,p} is a closed subspace of Waterman-Shiba space αBV^(p).

Keywords

### History

• Receive Date: 25 August 2019
• Revise Date: 14 February 2021
• Accept Date: 06 April 2021