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.



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