Blower, Gordon (2000) *Maximal functions for groups of operators.* Proceedings of the Edinburgh Mathematical Society, 43 (1). pp. 57-71. ISSN 0013-0915

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: | Journal Article |
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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: | 09 Feb 2018 00:05 |

Identification Number: | |

URI: | http://eprints.lancs.ac.uk/id/eprint/19329 |

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