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New criteria for the $H^\infty$-calculus and the Stokes operator on bounded Lipschitz domains

Kunstmann, Peer Christian; Weis, Lutz


We show that the Stokes operator A on the Helmholtz space Lp (Ω) for a bounded Lipschitz domain Ω ⊂ Rd, d ≥ 3, has a bounded H ∞- calculus if |1p − 1/2| ≤ 1/2d . Our proof uses a new comparison theorem A and the Dirichlet Laplace −∆ on Lp(Ω)d, which is based on “off-diagonal” estimates of the Littlewood-Paley decompositions of A and −∆. This comparison theorem can be formulated for rather general sectorial operators and is well suited to extrapolate the H ∞-calculus from L2(U ) to the Lp(U )-scale or part of it. It also gives some information on coincidence of domains of fractional powers.

Volltext §
DOI: 10.5445/IR/1000060560
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsjahr 2016
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000060560
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 25 S.
Serie CRC 1173 ; 2016/26
Schlagwörter sectorial operators, bounded H ∞-calculus, Littlewood-Paley operators, domains of fractional powers, Stokes operator
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