Real interpolation of domains of sectorial operators on Lp-spaces

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