Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Minimax Theory and its Applications 04 (2019), No. 1, 151--160Copyright Heldermann Verlag 2019 Dual of the Class of HKr Integrable Functions Paul Musial Dept. of Mathematics and Computer Science, Chicago University, 9501 S. King Drive, Chicago, IL 60628, U.S.A. pmusial@csu.edu Francesco Tulone Dept. of Mathematics and Computer Science, Palermo University, Viale delle Scienze, 90128 Palermo, Italy francesco.tulone@unipa.it [Abstract-pdf] We define for $1 \leq r < \infty$ 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. Keywords: Lr-Henstock-Kurzweil integral, HKr-dual, HKr-norm. MSC: 26A39 [ Fulltext-pdf  (101  KB)] for subscribers only.