Operador multiplicación sobre el espacio de funciones de p-variación acotada en el sentido de wiener

Abstract

In this work, we make an exhaustive study of the properties of the spaces of function of bounded p−variation in Wiener’s sense which is denoted by W BVp[a, b]. Furthermore, we establish the properties of the multiplication operator over this space. We characterize all the functions u ∈ W BVp[0, 1] which define invertible multiplication operators, compact and Fredholm multiplication operator Mu on W BVp[0, 1]. Moreover, it is characterized when Mu has finite range and closed range on W BVp[0, 1]. The results obtained by Astudillo- Villaba, Castillo and Ramos-Fern´andez in are presented.