Research output: Contribution in Book/Report/Proceedings › Chapter

Published

Publication date | 2010 |
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Host publication | The AMSI-ANU Workshop on Spectral Theory and Harmonic Analysis : The Australian National University, Canberra, July 2009 |

Editors | Andrew Hassell, Alan McIntosh, Robert Taggart |

Place of Publication | Canberra |

Publisher | Australian National University |

Pages | 105-114 |

Number of pages | 10 |

Volume | 44 |

Edition | 44 |

ISBN (Print) | 0 7315 5208 3 |

<mark>Original language</mark> | English |

Name | Proceedings of the Centre for Mathematics and its Applications |
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Publisher | Australian National University |

Suppose that 1<p\leq \infty (\Omega ,\mu) is a \sigma finite measure space and E is a closed subspace of Labesgue Bochner space L^p(\Omega; E) consisting of function oon \Omega that take their values in some complex Banach space X. Suppose that -A is invertible and generates a bounded hlomorphic semigroup T_z on E. If 0<\alpha <1, and f belongs to the domain of A^\alpha, then the maximal function \sup_z|T_zf|, where the supremum is taken over any sector contained in the sector of holomorphy, belongs to L^p. This extends an earlier result of Blower and Doust.