Blower, Gordon (2002) *Maximal functions and subordination for operator groups.* Proceedings of the Edinburgh Mathematical Society, 45 (1). pp. 27-42. ISSN 0013-0915

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Official URL: http://dx.doi.org/10.1017/S0013091500000535

## Abstract

Let E be a UMD Banach space and L a positive and self-adjoint operator in L^2 of Laplace type such that the imaginary powers L^{-it} form a C_0 group of exponential growth on L^p(E). Suppose that G is holomorphis inside and on the boundary os a suitable sector. Then G(tL) defines a bounded family of linear operators on L^p(E); the maximal operator f->sup | G(tL)f| os bounded on the domain of log L. These hypotheses hold for the maximal solution operators for the heat, wave and Schroedinger operators, and for Cesaro sums.

Item Type: | Article |
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Journal or Publication Title: | Proceedings of the Edinburgh Mathematical Society |

Additional Information: | AMS 2000 classification 47D03; 42B25; 47D09 The final, definitive version of this article has been published in the Journal, Proceedings of the Edinburgh Mathematical Society, 45 (1), pp 27-42 2002, © 2002 Cambridge University Press. |

Uncontrolled Keywords: | maximal functions ; transference ; UMD Banach spaces |

Subjects: | Q Science > QA Mathematics |

Departments: | Faculty of Science and Technology > Mathematics and Statistics |

ID Code: | 1693 |

Deposited By: | Professor Gordon Blower |

Deposited On: | 18 Feb 2008 10:06 |

Refereed?: | Yes |

Published?: | Published |

Last Modified: | 20 Jan 2016 01:02 |

Identification Number: | |

URI: | http://eprints.lancs.ac.uk/id/eprint/1693 |

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