The space of Henstock integrable functions of two variables
We consider the space of Henstock integrable functions of two variables. Equipped with the Alexiewicz norm the space is proved to be barrelled. We give a partial description of its dual. We show by an example that the dual can't be described in a manner analogous to the one-dimensional case, si...
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| Format: | Article |
| Language: | English |
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Wiley
1988-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171288000043 |
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| _version_ | 1832558635800068096 |
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| author | Krzysztof Ostaszewski |
| author_facet | Krzysztof Ostaszewski |
| author_sort | Krzysztof Ostaszewski |
| collection | DOAJ |
| description | We consider the space of Henstock integrable functions of two variables. Equipped with the Alexiewicz norm the space is proved to be barrelled. We give a partial description of its dual. We show by an example that the dual can't be described in a manner analogous to the one-dimensional case, since in two variables there exist functions whose distributional partials are measures and which are not multipliers for Henstock integrable functions. |
| format | Article |
| id | doaj-art-110a5791f0e4475781524f780219f15f |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1988-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-110a5791f0e4475781524f780219f15f2025-02-03T01:31:50ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251988-01-01111152110.1155/S0161171288000043The space of Henstock integrable functions of two variablesKrzysztof Ostaszewski0University of Louisville, Department of Mathematics, Louisville 40292, KY, USAWe consider the space of Henstock integrable functions of two variables. Equipped with the Alexiewicz norm the space is proved to be barrelled. We give a partial description of its dual. We show by an example that the dual can't be described in a manner analogous to the one-dimensional case, since in two variables there exist functions whose distributional partials are measures and which are not multipliers for Henstock integrable functions.http://dx.doi.org/10.1155/S0161171288000043Henstock integralbarrelbarrelled spacenormed spacecontinuous linear functionals. |
| spellingShingle | Krzysztof Ostaszewski The space of Henstock integrable functions of two variables International Journal of Mathematics and Mathematical Sciences Henstock integral barrel barrelled space normed space continuous linear functionals. |
| title | The space of Henstock integrable functions of two variables |
| title_full | The space of Henstock integrable functions of two variables |
| title_fullStr | The space of Henstock integrable functions of two variables |
| title_full_unstemmed | The space of Henstock integrable functions of two variables |
| title_short | The space of Henstock integrable functions of two variables |
| title_sort | space of henstock integrable functions of two variables |
| topic | Henstock integral barrel barrelled space normed space continuous linear functionals. |
| url | http://dx.doi.org/10.1155/S0161171288000043 |
| work_keys_str_mv | AT krzysztofostaszewski thespaceofhenstockintegrablefunctionsoftwovariables AT krzysztofostaszewski spaceofhenstockintegrablefunctionsoftwovariables |