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A maximal theorem for holomorphic semigroups.

Research output: Contribution to journalJournal articlepeer-review

<mark>Journal publication date</mark>03/2005
<mark>Journal</mark>The Quarterly Journal of Mathematics
Issue number1
Number of pages10
Pages (from-to)21-30
Publication StatusPublished
<mark>Original language</mark>English


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.

Bibliographic note

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