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ISSN 1088-6850(e) ISSN 0002-9947(p)

Bounded $H_\infty$ -calculus for pseudodifferential operators and applications to the Dirichlet-Neumann operator

Author(s): J. Escher; J. Seiler
Journal: Trans. Amer. Math. Soc. 360 (2008), 3945-3973.
MSC (2000): Primary 47G30; Secondary 35R35, 47A60, 58D25
Posted: March 13, 2008
MathSciNet review: 2395160
Retrieve article in: PDF

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Abstract: Operators of the form with a pseudodifferential symbol $a(x,\xi)$ belonging to the Hörmander class $S^m_{1,\delta}$ , , $0\le\delta<1$ , and certain perturbations are shown to possess a bounded $H_\infty$ -calculus in Besov-Triebel-Lizorkin and certain subspaces of Hölder spaces, provided is suitably elliptic. Applications concern pseudodifferential operators with mildly regular symbols and operators on manifolds of low regularity. An example is the Dirichlet-Neumann operator for a compact domain with $\mathcal{C}^{1+r}$ -boundary.

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