A new characterization of the dual space of the HK-integrable functions-Reference-Cited by-同舟云学术

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

Published:2024 Issue:4 Volume:9 Page:8250-8261
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Arredondo Juan H.¹,Montaño Genaro¹,Mendoza Francisco J.²

Affiliation:

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

Abstract

<abstract><p>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.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

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