H∞ functional calculus in real interpolation spaces

Let A be a linear closed densely defined operator in a complex Banach space X. If A is of type omega (i.e. the spectrum of A is contained in a sector of angle 2 omega, symmetric around the real positive axis, and parallel to lambda(lambda I - A)(-1)parallel to is bounded outside every larger sector) and has a bounded inverse, then A has a bounded H-infinity functional calculus in the real interpolation spaces between X and the domain of the operator itself.