Irregular amalgams
The amalgam of Lp and ℓq consists of those functions for which the sequence of Lp-norms over the intervals [n,n+1) is in ℓq. These spaces (Lp,ℓq) have been studied in several recent papers. Here we replace the intervals [n,n+1) by a cover α={In;n∈Z} of the real line consisting of disjoint half-open...
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| Format: | Article |
| Language: | English |
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Wiley
1986-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171286000418 |
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| _version_ | 1832548506315784192 |
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| author | James Stewart Saleem Watson |
| author_facet | James Stewart Saleem Watson |
| author_sort | James Stewart |
| collection | DOAJ |
| description | The amalgam of Lp and ℓq consists of those functions for which the sequence of Lp-norms over the intervals [n,n+1) is in ℓq. These spaces (Lp,ℓq) have been studied in several recent papers. Here we replace the intervals [n,n+1) by a cover α={In;n∈Z} of the real line consisting of disjoint half-open intervals In each of the form [a,b), and investigate which properties of (Lp,ℓq) carry over to these irregular amalgams (Lp,ℓq)α. In particular, we study how (Lp,ℓq)α varies as p, q, and α vary and determine conditions under which translation is continuous. |
| format | Article |
| id | doaj-art-ed78495365114987bfd8e1af2ec69224 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1986-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-ed78495365114987bfd8e1af2ec692242025-02-03T06:14:01ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251986-01-019233134010.1155/S0161171286000418Irregular amalgamsJames Stewart0Saleem Watson1Department of Mathematics, McMaster University, Hamilton, Ontario L8S 4K1, CanadaDepartment of Mathematics, Pennsylvania State University, Media, Pennsylvania 19063, USAThe amalgam of Lp and ℓq consists of those functions for which the sequence of Lp-norms over the intervals [n,n+1) is in ℓq. These spaces (Lp,ℓq) have been studied in several recent papers. Here we replace the intervals [n,n+1) by a cover α={In;n∈Z} of the real line consisting of disjoint half-open intervals In each of the form [a,b), and investigate which properties of (Lp,ℓq) carry over to these irregular amalgams (Lp,ℓq)α. In particular, we study how (Lp,ℓq)α varies as p, q, and α vary and determine conditions under which translation is continuous.http://dx.doi.org/10.1155/S0161171286000418amalgam. |
| spellingShingle | James Stewart Saleem Watson Irregular amalgams International Journal of Mathematics and Mathematical Sciences amalgam. |
| title | Irregular amalgams |
| title_full | Irregular amalgams |
| title_fullStr | Irregular amalgams |
| title_full_unstemmed | Irregular amalgams |
| title_short | Irregular amalgams |
| title_sort | irregular amalgams |
| topic | amalgam. |
| url | http://dx.doi.org/10.1155/S0161171286000418 |
| work_keys_str_mv | AT jamesstewart irregularamalgams AT saleemwatson irregularamalgams |