
Minimax Theory and its Applications 04 (2019), No. 1, 151160 Copyright Heldermann Verlag 2019 Dual of the Class of HK_{r} 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 [Abstractpdf] We define for $1 \leq r < \infty$ a norm for the class of functions which are HenstockKurzweil 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: LrHenstockKurzweil integral, HKrdual, HKrnorm. MSC: 26A39 [ Fulltextpdf (101 KB)] for subscribers only. 