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: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2018-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2018/8169565 |
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| _version_ | 1832567218682986496 |
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| author | Tomás Pérez Becerra Juan Alberto Escamilla Reyna Daniela Rodríguez Tzompantzi Jose Jacobo Oliveros Oliveros Khaing Khaing Aye |
| author_facet | Tomás Pérez Becerra Juan Alberto Escamilla Reyna Daniela Rodríguez Tzompantzi Jose Jacobo Oliveros Oliveros Khaing Khaing Aye |
| author_sort | Tomás Pérez Becerra |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-1f9c98b5cfa147ae88cfda4263446248 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-1f9c98b5cfa147ae88cfda42634462482025-02-03T01:02:01ZengWileyJournal 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 |
| 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 |
| title | 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_short | 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 |
| url | http://dx.doi.org/10.1155/2018/8169565 |
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