Functional calculus on real interpolation spaces for generators of   $C_{0}$-groups
  We study functional calculus properties of $C_{0}$-groups on real interpolation spaces, using transference principles. We obtain interpolation versions of the classical transference principle for bounded groups and of a recent transference principle for unbounded groups. Then we show that each group generator on a Banach space has a bounded $H^{\infty}_{1}$-calculus on real interpolation spaces. Additional results are derived from this. 
Markus Haase and Jan Rozendaal
math.FA math.OA