Bounded $H_\infty$-calculus for pseudodifferential operators and applications to the Dirichlet-Neumann operator
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Abstract:
Operators of the form $A=a(x,D)+K$ with a pseudodifferential symbol $a(x,\xi )$ belonging to the Hörmander class $S^m_{1,\delta }$, $m>0$, $0\le \delta <1$, and certain perturbations $K$ are shown to possess a bounded $H_\infty$-calculus in Besov-Triebel-Lizorkin and certain subspaces of Hölder spaces, provided $a$ 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.References
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Additional Information
- J. Escher
- Affiliation: Institut für Angewandte Mathematik, Universität Hannover, Welfengarten 1, 30167 Hannover, Germany
- Email: escher@ifam.uni-hannover.de
- J. Seiler
- Affiliation: Institut für Angewandte Mathematik, Universität Hannover, Welfengarten 1, 30167 Hannover, Germany
- Email: seiler@ifam.uni-hannover.de
- Received by editor(s): November 17, 2005
- Published electronically: March 13, 2008
- © Copyright 2008 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 360 (2008), 3945-3973
- MSC (2000): Primary 47G30; Secondary 35R35, 47A60, 58D25
- DOI: https://doi.org/10.1090/S0002-9947-08-04589-3
- MathSciNet review: 2395160