Dual of the Class of HKr Integrable Functions
- Authors: Musial, P; Tulone, F
- Publication year: 2019
- Type: Articolo in rivista
- OA Link: http://hdl.handle.net/10447/423776
Abstract
We define for 1 <= r < infinity a norm for the class of functions which are Henstock-Kurzweil integrable in the L-r sense. We then establish that the dual in this norm is isometrically isomorphic to L-r' and is therefore a Banach space, and in the case r = 2, a Hilbert space. Finally, we give results pertaining to convergence and weak convergence in this space.