| Title:
|
A full characterization of multipliers for the strong $\rho$-integral in the euclidean space (English) |
| Author:
|
Tuo-Yeong, Lee |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
54 |
| Issue:
|
3 |
| Year:
|
2004 |
| Pages:
|
657-674 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study a generalization of the classical Henstock-Kurzweil integral, known as the strong $\rho $-integral, introduced by Jarník and Kurzweil. Let $(\mathcal S_{\rho } (E), \Vert \cdot \Vert )$ be the space of all strongly $\rho $-integrable functions on a multidimensional compact interval $E$, equipped with the Alexiewicz norm $\Vert \cdot \Vert $. We show that each element in the dual space of $(\mathcal S_{\rho } (E), \Vert \cdot \Vert )$ can be represented as a strong $\rho $-integral. Consequently, we prove that $fg$ is strongly $\rho $-integrable on $E$ for each strongly $\rho $-integrable function $f$ if and only if $g$ is almost everywhere equal to a function of bounded variation (in the sense of Hardy-Krause) on $E$. (English) |
| Keyword:
|
strong $\rho $-integral |
| Keyword:
|
multipliers |
| Keyword:
|
dual space |
| MSC:
|
26A39 |
| MSC:
|
46E99 |
| MSC:
|
46G10 |
| idZBL:
|
Zbl 1080.26007 |
| idMR:
|
MR2086723 |
| . |
| Date available:
|
2009-09-24T11:16:15Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127918 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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