*Ian
Doust's *i*nformation 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 *L*^{p}(
\Omega ,μ ) for some 1 < *p* < \infty , and let *-A*
be an invertible operator that is the generator of
a bounded
holomorphic semigroup * T*_{t}
on *X*. Then for each 0 < \alpha < 1 the maximal function
sup_{t > 0} | *T*_{t}f(x) |
belongs to * L*^{p}(\Omega ,μ)
for each *f* in the domain of *A*^{\alpha}. If
moreover *iA* generates a
bounded *C*_{0}-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.