Remarks on Functional Calculus for Perturbed First-order Dirac Operators

DOI10.1007/978-3-319-06266-2_2zbMath1341.47019arXiv1303.5047OpenAlexW2500617969MaRDI QIDQ2944068

Sebastian Stahlhut, Pascal Auscher

Publication date: 7 September 2015

Published in: Operator Theory in Harmonic and Non-commutative Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1303.5047

zbMATH Keywords

Dirac operatorscoercivity conditions\(R\)-bisectorial operatorsdifferential operators with bounded measurable coefficientsextrapolation of norm inequalitieskernel/range decomposition

Mathematics Subject Classification ID

Functional calculus for linear operators (47A60) General theory of partial differential operators (47F05) Harmonic analysis and PDEs (42B37)

Related Items (3)

\(L^p\)-analysis of the Hodge-Dirac operator associated with Witten Laplacians on complete Riemannian manifolds ⋮ Hodge-Dirac, Hodge-Laplacian and Hodge-Stokes operators in \(L^p\) spaces on Lipschitz domains ⋮ Conical square function estimates and functional calculi for perturbed Hodge-Dirac operators in \(L^p\)

Cites Work

• Unnamed Item
• Holomorphic functional calculus of Hodge-Dirac operators in \(L ^{p }\)
• Solvability of elliptic systems with square integrable boundary data
• Quadratic estimates and functional calculi of perturbed Dirac operators
• Perturbation and interpolation theorems for the \(H^\infty\)-calculus with applications to differential operators
• The Kato square root problem for higher order elliptic operators and systems on \(\mathbb{R}^n\)
• The solution of the Kato square root problem for second order elliptic operators on \(\mathbb R^n\).
• Kato's square root problem in Banach spaces
• On necessary and sufficient conditions for 𝐿^{𝑝}-estimates of Riesz transforms associated to elliptic operators on ℝⁿ and related estimates
• Extrapolation of the functional calculus of generalized Dirac operators and related embedding and Littlewood-Paley-type theorems. I
• On a quadratic estimate related to the Kato conjecture and boundary value problems
• Stability results on interpolation scales of quasi-Banach spaces and applications
• The square root problem of Kato in one dimension, and first order elliptic systems
• The \(H^\infty\)-calculus and sums of closed operators

This page was built for publication: Remarks on Functional Calculus for Perturbed First-order Dirac Operators