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A functional calculus description of real interpolation spaces for sectorial operators

Markus Haase (2005)

Studia Mathematica

For a holomorphic function ψ defined on a sector we give a condition implying the identity ( X , ( A α ) ) θ , p = x X | t - θ R e α ψ ( t A ) L p ( ( 0 , ) ; 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.

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