A functional calculus description of real interpolation spaces for sectorial operators

Markus Haase¹

¹ Scuola Normale Superiore Piazza dei Cavalieri 7 I-56126 Pisa, Italy

Studia Mathematica, Tome 171 (2005) no. 2, pp. 177-195

Résumé

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.

Détail

DOI : 10.4064/sm171-2-4

Keywords: holomorphic function psi defined sector condition implying identity scr alpha theta mid theta mathop alpha psi ast infty where sectorial operator banach space yields common descriptions real interpolation spaces sectorial operators allows easy proofs moment inequalities reiteration results fractional powers