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Abstract

For a holomorphic function $\psi$ defined on a sector we give a condition implying the identity $$(X,{\scr D}(A^\alpha))_{\theta,p} = \{ x\in X \mid t^{-\theta \mathop{\rm Re} \alpha} \psi(tA) \in {\bf L}^p_{\ast}((0,\infty);X)\} $$ where $A$ is a sectorial operator on a Banach space $X$. This yields all common descriptions of the real interpolation spaces for sectorial operators and allows easy proofs of the moment inequalities and reiteration results for fractional powers.