Ian Doust's information pages

A maximal theorem for holomorphic semigroups

Q.J. Math, 56 (2005), 21-30.

Gordon Blower and Ian Doust

Contact details:
Blower: Department of Mathematics and Statistics, Lancaster University, Lancaster, LA1 4YF, UK.
Doust: School of Mathematics, University of New South Wales, Sydney NSW 2052, Australia

Email:  i.doust@unsw.edu.au

Abstract: 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.

The links below provide preprint versions of the paper. These may differ in minor ways from the final printed version, which is available from the OUP website.
The manuscript is available in several forms:

Please contact Ian if you have any trouble downloading the files, or if you would like an `official' reprint.