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

Juan H. Arredondo; Genaro Montaño; Francisco J. Mendoza; Juan H. Arredondo; Genaro Montaño; Francisco J. Mendoza

doi:10.3934/math.2024401

AIMS Mathematics

2024, Volume 9, Issue 4: 8250-8261. doi: 10.3934/math.2024401

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

1.
Department of Mathematics, Universidad Autónoma Metropolitana - Iztapalapa, Av. San Rafael Atlixco 186, CDMX, 09340, Mexico
2.
Faculty of Physical and Mathematical Sciences, Benemérita Universidad Autónoma de Puebla, Av. San Claudio y 18 Sur S/N, Puebla, Puebla, 72570, Mexico

Received: 02 December 2023 Revised: 27 January 2024 Accepted: 30 January 2024 Published: 27 February 2024
MSC : 26A39, 26A45, 46B10

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.
- Henstock-Kurzweil integral,
- Banach dual space
Citation: Juan H. Arredondo, Genaro Montaño, Francisco J. Mendoza. A new characterization of the dual space of the HK-integrable functions[J]. AIMS Mathematics, 2024, 9(4): 8250-8261. doi: 10.3934/math.2024401

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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.

References

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