Real interpolation of domains of sectorial operators on Lp-spaces

Let A be a sectorial operator on a non-atomic Lp-space, 1 p <∞, whose resolvent consists of integral operators, or more generally, has a diffuse representation. Then the fractional domain spaces D(Aα) for α ∈ (0, 1) do not coincide with the real interpolation spaces of (Lq ,D(A)). As a consequence, we obtain that no such operator A has a bounded H∞-calculus if p = 1.  2005 Elsevier Inc. All rights reserved.