Skip Navigation

The Quarterly Journal of Mathematics 2005 56(1):21-30; doi:10.1093/qmath/hah024
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Blower, G.
Right arrow Articles by Doust, I.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The Author (2005). Published by Oxford University Press. All rights reserved. For Permissions please email: journals.permissions@oupjournals.org

A maximal theorem for holomorphic semigroups

Gordon Blower1 * and Ian Doust2 §

1 Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, 2 School of Mathematics, The University of New South Wales, NSW 2052, Australia

Let X be a closed linear subspace of the Lebesgue space Lp({Omega}; µ) for some 1 < p < {infty}, and let – A be an invertible operator that is the generator of a bounded holomorphic semigroup Tt on X. Then for each 0 < {alpha} < 1 the maximal function supt>0 |Ttf(x)| belongs to Lp({Omega}; µ) for each f in the domain of A{alpha}. If moreover iA generates a bounded C0-group and A has spectrum contained in (0, {infty}), then A has a bounded H{infty} functional calculus.

Received 15 September 2003. Revised 24 April 2004.

* Corresponding author; E-mail: g.blower{at}lancaster.ac.uk

§ E-mail: i.doust{at}unsw.edu.au


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer: Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.