A functional calculus description of real interpolation spaces for sectorial operators

• Autorzy: Markus Haase
• Języki publikacji: EN

Abstrakty

EN

For a holomorphic function ψ defined on a sector we give a condition implying the identity
$(X,𝒟(A^{α}))_{θ,p} = {x ∈ X | t^{-θ Re α} ψ(tA) ∈ L⁎^{p}((0,∞);X)}$
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.

Kategorie tematyczne

• 47D06: One-parameter semigroups and linear evolution equations
• 46B70: Interpolation between normed linear spaces
• 47B99: None of the above, but in this section
• 47A60: Functional calculus

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2005
• Tom: 171
• Numer: 2
• Strony: 177-195

Daty

wydano

2005

Twórcy

autor

Markus Haase

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

Identyfikatory

DOI

10.4064/sm171-2-4