Structure Theorem for Functionals in the Space ๐โฒ๐1,๐2
We introduce the space ๐๐1,๐2 of all ๐ถโ functions ๐ such that ๐ ๐ข๐|๐ผ|โค๐โ๐๐๐1๐๐ผ๐โโ and ๐ ๐ข๐|๐ผ|โค๐โ๐๐๐2๐๐ผ0๐ฅ0005๐๐โโ are finite for all ๐โโ0, ๐ผโโ๐0, where ๐1 and ๐2 are two weights satisfying the classical Beurling conditions. Moreover, we give a topological characterization of the space ๐๐1,๐2 without co...
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| Format: | Article |
| Language: | English |
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Wiley
2008-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2008/756834 |
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| author | Hamed M. Obiedat Wasfi A. Shatanawi Mohd M. Yasein |
| author_facet | Hamed M. Obiedat Wasfi A. Shatanawi Mohd M. Yasein |
| author_sort | Hamed M. Obiedat |
| collection | DOAJ |
| description | We introduce the space ๐๐1,๐2 of all ๐ถโ functions ๐ such that ๐ ๐ข๐|๐ผ|โค๐โ๐๐๐1๐๐ผ๐โโ and ๐ ๐ข๐|๐ผ|โค๐โ๐๐๐2๐๐ผ0๐ฅ0005๐๐โโ are finite for all ๐โโ0, ๐ผโโ๐0, where ๐1 and ๐2 are two weights satisfying
the classical Beurling conditions. Moreover, we give a topological
characterization of the space ๐๐1,๐2 without conditions on the derivatives. For functionals in the dual space ๐๎
๐1,๐2, we prove a structure
theorem by using the classical Riesz representation thoerem. |
| format | Article |
| id | doaj-art-44472438b4844078a3e3d478883edc32 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2008-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-44472438b4844078a3e3d478883edc322025-02-03T01:09:13ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252008-01-01200810.1155/2008/756834756834Structure Theorem for Functionals in the Space ๐โฒ๐1,๐2Hamed M. Obiedat0Wasfi A. Shatanawi1Mohd M. Yasein2Department of Mathematics, Hashemite University, P.O. Box 150459, Zarqa 13115, JordanDepartment of Mathematics, Hashemite University, P.O. Box 150459, Zarqa 13115, JordanDepartment of Mathematics, Hashemite University, P.O. Box 150459, Zarqa 13115, JordanWe introduce the space ๐๐1,๐2 of all ๐ถโ functions ๐ such that ๐ ๐ข๐|๐ผ|โค๐โ๐๐๐1๐๐ผ๐โโ and ๐ ๐ข๐|๐ผ|โค๐โ๐๐๐2๐๐ผ0๐ฅ0005๐๐โโ are finite for all ๐โโ0, ๐ผโโ๐0, where ๐1 and ๐2 are two weights satisfying the classical Beurling conditions. Moreover, we give a topological characterization of the space ๐๐1,๐2 without conditions on the derivatives. For functionals in the dual space ๐๎
๐1,๐2, we prove a structure theorem by using the classical Riesz representation thoerem.http://dx.doi.org/10.1155/2008/756834 |
| spellingShingle | Hamed M. Obiedat Wasfi A. Shatanawi Mohd M. Yasein Structure Theorem for Functionals in the Space ๐โฒ๐1,๐2 International Journal of Mathematics and Mathematical Sciences |
| title | Structure Theorem for Functionals in the Space ๐โฒ๐1,๐2 |
| title_full | Structure Theorem for Functionals in the Space ๐โฒ๐1,๐2 |
| title_fullStr | Structure Theorem for Functionals in the Space ๐โฒ๐1,๐2 |
| title_full_unstemmed | Structure Theorem for Functionals in the Space ๐โฒ๐1,๐2 |
| title_short | Structure Theorem for Functionals in the Space ๐โฒ๐1,๐2 |
| title_sort | structure theorem for functionals in the space ๐ ๐1 ๐2 |
| url | http://dx.doi.org/10.1155/2008/756834 |
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