The Banach space -valued BMO, Carleson's condition, and paraproducts
| dc.creator | Hytönen, Tuomas | |
| dc.creator | Weis, Lutz | |
| dc.date | 2008-11-20 | |
| dc.date.accessioned | 2026-07-07T10:19:46Z | |
| dc.date.available | 2026-07-07T10:19:46Z | |
| dc.description | We define a scale of L^q Carleson norms, all of which characterize the membership of a function in BMO. The phenomenon is analogous to the John-Nirenberg inequality, but on the level of Carleson measures. The classical Carleson condition corresponds to the L^2 case in our theory. The result is applied to give a new proof for the L^p-boundedness of paraproducts with a BMO symbol. A novel feature of the argument is that all p are covered at once in a completely interpolation-free manner. This is achieved by using the L^1 Carleson norm, and indicates the usefulness of this notion. Our approach is chosen so that all these results extend in a natural way to the case of X-valued functions, where X is a Banach space with the UMD property. | |
| dc.description | 14 pages, submitted | |
| dc.identifier | https://arxiv.org/abs/0811.3333 | |
| dc.identifier | http://arxiv.org/abs/0811.3333 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/174628 | |
| dc.subject | Functional Analysis | |
| dc.subject | 42B35; 42B20; 42B25; 46E40 | |
| dc.title | The Banach space -valued BMO, Carleson's condition, and paraproducts | |
| dc.type | text |