Blower, Gordon (2000) Maximal functions for groups of operators. Proceedings of the Edinburgh Mathematical Society, 43 (1). pp. 57-71. ISSN 0013-0915
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Official URL: http://dx.doi.org/10.1017/S0013091500020691
Abstract
Let Δ be the Laplace operator on d and 1 < δ < 2. Using transference methods we show that, for max {q, q/(q – 1)} < 4d/(2d + 1 – δ), the maximal function for the Schrödinger group is in Lq, for f Lq with Δδ/2 f Lq. We obtain a similar result for the Airy group exp it Δ3/2. An abstract version of these results is obtained for bounded C0-groups eitL on subspaces of Lp spaces. Certain results extend to maximal functions defined for functions with values in U M D Banach spaces.
| Item Type: | Article |
|---|---|
| Journal or Publication Title: | Proceedings of the Edinburgh Mathematical Society |
| Additional Information: | http://journals.cambridge.org/action/displayJournal?jid=PEM The final, definitive version of this article has been published in the Journal, Proceedings of the Edinburgh Mathematical Society, 43 (1), pp 57-71 2000, © 2000 Cambridge University Press. |
| Subjects: | Q Science > QA Mathematics |
| Departments: | Faculty of Science and Technology > Mathematics and Statistics |
| ID Code: | 19329 |
| Deposited By: | ep_ss_importer |
| Deposited On: | 18 Nov 2008 10:53 |
| Refereed?: | Yes |
| Published?: | Published |
| Last Modified: | 26 Jul 2012 15:28 |
| Identification Number: | |
| URI: | http://eprints.lancs.ac.uk/id/eprint/19329 |
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