TY  - INPR
A1  - Denk, Robert
A1  - Krainer, Thomas
T1  - R-Boundedness, pseudodifferential operators, and maximal regularity for some classes of partial differential operators
N2  - It is shown that an elliptic scattering operator A on a compact manifold with boundary with operator valued coefficients in the morphisms of a bundle of Banach spaces of class (HT ) and Pisier’s property (α) has maximal regularity (up to a spectral shift), provided that the spectrum of the principal symbol of A on the scattering cotangent bundle avoids the right half-plane. This is accomplished by representing the resolvent in terms of pseudodifferential operators with R-bounded symbols, yielding by an iteration argument the R-boundedness of λ(A − λ)−1 in R(λ)≥ τ for some τ ∈ IR. To this end, elements of a symbolic and operator calculus of pseudodifferential operators with R-bounded symbols are introduced. The significance of this method for proving maximal regularity results for partial differential operators is underscored by considering also a more elementary situation of anisotropic elliptic operators on Rd with operator valued coefficients.
T3  - Preprint - (2006) 14 
Y1  - 2009
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/2848
UR  - https://nbn-resolving.org/urn:nbn:de:kobv:517-opus-30147
ER  -