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A functional calculus description of real interpolation spaces for sectorial operators

100%

Haase M.

Studia Mathematica

2005

tom 171

nr 2

177-195

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.

Domain characterizations of certain functions of power-bounded operators

63%

Haase M., Tomilov Y.

Studia Mathematica

2010

tom 196

nr 3

265-288

We create a general framework for describing domains of functions of power-bounded operators given by power series with log-convex coefficients. This sheds new light on recent results of Assani, Derriennic, Lin and others. In particular, we resolve an open problem regarding the "one-sided ergodic Hilbert transform" formulated in a 2001 paper by Derriennic and Lin.

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2 Studia Mathematica

2 Haase M.

1 Tomilov Y.

1 2010

1 2005

Wyniki wyszukiwania

A functional calculus description of real interpolation spaces for sectorial operators

Domain characterizations of certain functions of power-bounded operators