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A maximal theorem for holomorphic semigroups.

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

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    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
    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: 19 Nov 2013 09:52
    Identification Number:
    URI: http://eprints.lancs.ac.uk/id/eprint/1695

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