Dual of the Class of HK Integrable Functions

Authors

  • Paul Musial,Francesco Tulone Author

Keywords:

Lr-Henstock-Kurzweil integral, HKr-dual, HKr-norm.

Abstract

We define for 1 r < a norm for the class of functions which are Henstock-Kurzweil integrable in the Lr sense. We then establish that the dual in this norm is isometrically isomorphic to Lr′ 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.

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Published

2019-01-05

Issue

Vol. 4 No. 1 (2019): volume 4 issue 1 (2019)

Section

Articles

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How to Cite

Dual of the Class of HK Integrable Functions. (2019). Minimax Theory and Its Applications, 4(1), 151–160. https://journalmta.com/index.php/jmta/article/view/59