Blower, Gordon and Doust, Ian (2005) A maximal theorem for holomorphic semigroups. Quarterly Journal of Mathematics (Oxford), 56 (1). pp. 21-30.
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: ||Quarterly Journal of Mathematics (Oxford)|
|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|
|Last Modified: ||26 Jul 2012 15:17|
|Identification Number: |
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