Rs-bounded H∞-calculus for sectorial operators via generalized Gaussian estimates

Rs-bounded H∞-calculus for sectorial operators via generalized Gaussian estimates

We show that, for negative generators of analytic semigroups, a bounded H∞‐calculus self‐improves to an Rs‐bounded H∞‐calculus in an appropriate scale of Lp‐spaces if the semigroup satisfies suitable generalized Gaussian estimates. As application of our result we obtain that large classes of differe...

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Veröffentlicht in:Mathematische Nachrichten 2015-08, Vol.288 (11-12), p.1371-1387
Hauptverfasser: Kunstmann, Peer Christian, Ullmann, Alexander
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Sprache:eng
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42B25
47A60
47B38
47D06
Calderón-Zygmund theory
elliptic operators
Functional calculus
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container_title Mathematische Nachrichten
container_volume 288
creator Kunstmann, Peer Christian
Ullmann, Alexander
description We show that, for negative generators of analytic semigroups, a bounded H∞‐calculus self‐improves to an Rs‐bounded H∞‐calculus in an appropriate scale of Lp‐spaces if the semigroup satisfies suitable generalized Gaussian estimates. As application of our result we obtain that large classes of differential operators have an Rs‐bounded H∞‐calculus.
doi_str_mv 10.1002/mana.201300132
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subjects 42B25
47A60
47B38
47D06
Calderón-Zygmund theory
elliptic operators
Functional calculus
title Rs-bounded H∞-calculus for sectorial operators via generalized Gaussian estimates
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