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Maximal functions for groups of operators.

Research output: Contribution to journalJournal article

Published

Journal publication date02/2000
JournalProceedings of the Edinburgh Mathematical Society
Journal number1
Volume43
Number of pages15
Pages57-71
Original languageEnglish

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.

Bibliographic note

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.