Blower, Gordon and Doust, Ian and Taggart, Robert (2010) A maximal theorem for holomorphic semigroups on vectorvalued spaces. In: The AMSIANU Workshop on Spectral Theory and Harmonic Analysis : The Australian National University, Canberra, July 2009. Proceedings of the Centre for Mathematics and its Applications, 44 (44). Australian National University, Canberra, pp. 105114. ISBN 0 7315 5208 3

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Abstract
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_zT_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.
Item Type:  Contribution in Book/Report/Proceedings 

Uncontrolled Keywords:  /dk/atira/pure/researchoutput/libraryofcongress/qa 
Subjects:  
Departments:  Faculty of Science and Technology > Mathematics and Statistics 
ID Code:  28029 
Deposited By:  Professor Gordon Blower 
Deposited On:  02 Nov 2009 11:38 
Refereed?:  No 
Published?:  Published 
Last Modified:  25 Feb 2020 04:49 
URI:  https://eprints.lancs.ac.uk/id/eprint/28029 
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