Maximal functions for groups of operators.

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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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:

Journal 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.

Uncontrolled Keywords:

/dk/atira/pure/subjectarea/asjc/2600/2600

Subjects:

?? general mathematicsmathematics(all)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