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Research Article | Open Access

A new characterization of the dual space of the HK-integrable functions

Juan H. Arredondo1, Genaro Montaño1, Francisco J. Mendoza2( )
Department of Mathematics, Universidad Autónoma Metropolitana - Iztapalapa, Av. San Rafael Atlixco 186, CDMX, 09340, Mexico
Faculty of Physical and Mathematical Sciences, Benemérita Universidad Autónoma de Puebla, Av. San Claudio y 18 Sur S/N, Puebla, Puebla, 72570, Mexico
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Abstract

We construct the Henstock-Kurzweil (HK) integral as an extension of a linear form initially defined on L 1 , but which is not continuous in this space. This gives us an alternative way to prove existing results. In particular, we give a new characterization of the dual space of Henstock-Kurzweil integrable functions in terms of a quotient space.

Keywords

Henstock-Kurzweil integralBanach dual space
CLC number: 26A39, 26A45, 46B10

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AIMS Mathematics
Volume 9 Issue 4,
April 2024
Pages 8250-8261
DOI: 10.3934/math.2024401

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Cite this article:
Arredondo JH, Montaño G, Mendoza FJ. A new characterization of the dual space of the HK-integrable functions. AIMS Mathematics, 2024, 9(4): 8250-8261. https://doi.org/10.3934/math.2024401

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Received: 02 December 2023
Revised: 27 January 2024
Accepted: 30 January 2024
Published: 15 April 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)