Blower, Gordon and Doust, Ian (2005) *A maximal theorem for holomorphic semigroups.* The Quarterly Journal of Mathematics, 56 (1). pp. 21-30. ISSN 0033-5606

Official URL: http://dx.doi.org/10.1093/qmath/hah024

## Abstract

Let X be a closed linear subspace of the Lebesgue space L^p(Omega ; mu); let -A be an invertible linear operator that is the generator of abounded holomorphic semigroup T_t on X. The for each 0<a<1 the maximal operator sup |T_tf(x)| belongs to L^p for each f in the domain of A^a. If moreover iA generates a bounded C_0 group and A has spectrum contained in the positive real semi axis, then A has a bounded H infinity functional calculus.

Item Type: | Article |
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Journal or Publication Title: | The Quarterly Journal of Mathematics |

Additional Information: | The definitive publisher-authenticated version: Blower, Gordon and Doust, Ian A maximal theorem for holomorphic semigroups. Quarterly Journal of Mathematics (Oxford) 2005 56 (1): 21-30 is available online at: http://qjmath.oxfordjournals.org/cgi/reprint/56/1/21 |

Uncontrolled Keywords: | UMD Banach spaces ; transference ; functional calculus |

Subjects: | Q Science > QA Mathematics |

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

ID Code: | 1695 |

Deposited By: | Professor Gordon Blower |

Deposited On: | 18 Feb 2008 09:53 |

Refereed?: | Yes |

Published?: | Published |

Last Modified: | 08 Dec 2016 01:15 |

Identification Number: | |

URI: | http://eprints.lancs.ac.uk/id/eprint/1695 |

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