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

Official URL: https://doi.org/10.1093/qmath/hah024

## 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:

Journal 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:

/dk/atira/pure/researchoutput/libraryofcongress/qa

Subjects:

Departments:

ID Code:

1695

Deposited By:

Deposited On:

18 Feb 2008 09:53

Refereed?:

Yes

Published?:

Published

Last Modified:

13 May 2021 00:20