A Riesz Representation Theorem for the Space of Henstock Integrable Vector-Valued Functions

Using a bounded bilinear operator, we define the Henstock-Stieltjes integral for vector-valued functions; we prove some integration by parts theorems for Henstock integral and a Riesz-type theorem which provides an alternative proof of the representation theorem for real functions proved by Alexiewi...

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Main Authors:	Tomás Pérez Becerra, Juan Alberto Escamilla Reyna, Daniela Rodríguez Tzompantzi, Jose Jacobo Oliveros Oliveros, Khaing Khaing Aye
Format:	Article
Language:	English
Published:	Hindawi Limited 2018-01-01
Series:	Journal of Function Spaces
Online Access:	http://dx.doi.org/10.1155/2018/8169565

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spelling	doaj-1f9c98b5cfa147ae88cfda42634462482020-11-24T22:45:59ZengHindawi LimitedJournal of Function Spaces2314-88962314-88882018-01-01201810.1155/2018/81695658169565A Riesz Representation Theorem for the Space of Henstock Integrable Vector-Valued FunctionsTomás Pérez Becerra0Juan Alberto Escamilla Reyna1Daniela Rodríguez Tzompantzi2Jose Jacobo Oliveros Oliveros3Khaing Khaing Aye4Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla, Puebla, PUE, MexicoFacultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla, Puebla, PUE, MexicoFacultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla, Puebla, PUE, MexicoFacultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla, Puebla, PUE, MexicoDepartment of Engineering Mathematics, Yangon Technological University, Yangon, MyanmarUsing a bounded bilinear operator, we define the Henstock-Stieltjes integral for vector-valued functions; we prove some integration by parts theorems for Henstock integral and a Riesz-type theorem which provides an alternative proof of the representation theorem for real functions proved by Alexiewicz.http://dx.doi.org/10.1155/2018/8169565
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Tomás Pérez Becerra Juan Alberto Escamilla Reyna Daniela Rodríguez Tzompantzi Jose Jacobo Oliveros Oliveros Khaing Khaing Aye
spellingShingle	Tomás Pérez Becerra Juan Alberto Escamilla Reyna Daniela Rodríguez Tzompantzi Jose Jacobo Oliveros Oliveros Khaing Khaing Aye A Riesz Representation Theorem for the Space of Henstock Integrable Vector-Valued Functions Journal of Function Spaces
author_facet	Tomás Pérez Becerra Juan Alberto Escamilla Reyna Daniela Rodríguez Tzompantzi Jose Jacobo Oliveros Oliveros Khaing Khaing Aye
author_sort	Tomás Pérez Becerra
title	A Riesz Representation Theorem for the Space of Henstock Integrable Vector-Valued Functions
title_short	A Riesz Representation Theorem for the Space of Henstock Integrable Vector-Valued Functions
title_full	A Riesz Representation Theorem for the Space of Henstock Integrable Vector-Valued Functions
title_fullStr	A Riesz Representation Theorem for the Space of Henstock Integrable Vector-Valued Functions
title_full_unstemmed	A Riesz Representation Theorem for the Space of Henstock Integrable Vector-Valued Functions
title_sort	riesz representation theorem for the space of henstock integrable vector-valued functions
publisher	Hindawi Limited
series	Journal of Function Spaces
issn	2314-8896 2314-8888
publishDate	2018-01-01
description	Using a bounded bilinear operator, we define the Henstock-Stieltjes integral for vector-valued functions; we prove some integration by parts theorems for Henstock integral and a Riesz-type theorem which provides an alternative proof of the representation theorem for real functions proved by Alexiewicz.
url	http://dx.doi.org/10.1155/2018/8169565
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A Riesz Representation Theorem for the Space of Henstock Integrable Vector-Valued Functions

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