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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1986-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171286000418 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |