Details
| Original language | English |
|---|---|
| Pages (from-to) | 3945-3973 |
| Number of pages | 29 |
| Journal | Transactions of the American Mathematical Society |
| Volume | 360 |
| Issue number | 8 |
| Publication status | Published - 13 May 2008 |
Abstract
Operators of the form A = a(x,D) + K with a pseudodifferential symbol a(x,ξ) belonging to the Hörmander class Sm 1,δ, m > 0, 0 ≤ δ < 1, and certain perturbations K are shown to possess a bounded H∞-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 C1+r-boundary.
Keywords
- Bounded H∞-calculus, Dirichlet-Neumann operator, Pseudodifferential operators
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Transactions of the American Mathematical Society, Vol. 360, No. 8, 13.05.2008, p. 3945-3973.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Bounded H∞-calculus for pseudodifferential operators and applications to the Dirichlet-Neumann operator
AU - Escher, Joachim
AU - Seiler, Jörg
PY - 2008/5/13
Y1 - 2008/5/13
N2 - Operators of the form A = a(x,D) + K with a pseudodifferential symbol a(x,ξ) belonging to the Hörmander class Sm 1,δ, m > 0, 0 ≤ δ < 1, and certain perturbations K are shown to possess a bounded H∞-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 C1+r-boundary.
AB - Operators of the form A = a(x,D) + K with a pseudodifferential symbol a(x,ξ) belonging to the Hörmander class Sm 1,δ, m > 0, 0 ≤ δ < 1, and certain perturbations K are shown to possess a bounded H∞-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 C1+r-boundary.
KW - Bounded H∞-calculus
KW - Dirichlet-Neumann operator
KW - Pseudodifferential operators
UR - http://www.scopus.com/inward/record.url?scp=67449163977&partnerID=8YFLogxK
U2 - 10.1090/S0002-9947-08-04589-3
DO - 10.1090/S0002-9947-08-04589-3
M3 - Article
AN - SCOPUS:67449163977
VL - 360
SP - 3945
EP - 3973
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
SN - 0002-9947
IS - 8
ER -