Real interpolation of domains of sectorial operators on \(L_p\)-spaces (Q2566117)

Let \(A\) be a sectorial operator on a non-atomic \(L_p\)-space, \(1\leq p<\infty\), whose resolvent consists of integral operators, or more generally, has a diffuse representation. Then the fractional domain spaces \(\mathcal{D}(A^\alpha)\) for \(\alpha\in (0,1)\) do not coincide with the real interpolation spaces of \((L_q,\mathcal{D}(A))\). As a consequence, we obtain that no such operator \(A\) has a bounded \(H^\infty\)-calculus if \(p=1\).