R-boundedness, pseudodifferential operators, and maximal regularity for some classes of partial differential operators

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dc.creatorDenk, Robert
dc.creatorKrainer, Thomas
dc.date2006-07-28
dc.date.accessioned2026-07-07T07:21:06Z
dc.date.available2026-07-07T07:21:06Z
dc.descriptionIt is shown that an elliptic scattering operator $A$ on a compact manifold with boundary with coefficients in the bounded operators 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 of the manifold avoids the right half-plane. This is deduced directly from a Seeley theorem, i.e. the resolvent is represented in terms of pseudodifferential operators with R-bounded symbols, thus showing by an iteration argument the R-boundedness of $λ(A-λ)^{-1}$ for $\Re(λ) \geq 0$. 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 $R^d$ with operator valued coefficients.
dc.description21 pages
dc.identifierhttps://arxiv.org/abs/math/0607735
dc.identifierhttp://arxiv.org/abs/math/0607735
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/115185
dc.subjectAnalysis of PDEs
dc.subjectFunctional Analysis
dc.subject35K40; 35K65; 35R20; 58J05
dc.titleR-boundedness, pseudodifferential operators, and maximal regularity for some classes of partial differential operators
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