Extrapolation of the functional calculus of generalized Dirac operators and related embedding and Littlewood-Paley-type theorems. I

DOI10.1017/S1446788700037940zbMath1156.47019MaRDI QIDQ3507538

Sergey Ajiev

Publication date: 20 June 2008

Published in: Journal of the Australian Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

functional calculusKato square root problemLittlewood-Paley theoremHilbert identityextrapolation of singular operatorsgeneralised Dirac operatorgeneralised embedding

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Geometry and structure of normed linear spaces (46B20) Functional calculus for linear operators (47A60) Perturbation theory of linear operators (47A55) General (adjoints, conjugates, products, inverses, domains, ranges, etc.) (47A05) Structure theory of linear operators (47A65) Banach spaces of continuous, differentiable or analytic functions (46E15) Nontrigonometric harmonic analysis (42C99) Inner product spaces and their generalizations, Hilbert spaces (46C99)

Related Items (2)

Remarks on Functional Calculus for Perturbed First-order Dirac Operators ⋮ Conical square function estimates and functional calculi for perturbed Hodge-Dirac operators in \(L^p\)

Cites Work

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• 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 \(\mathbb R^n\).
• \(L^p\) bounds for Riesz transforms and square roots associated to second order elliptic operators
• Calderón-Zygmund theory for non-integral operators and the \(H^\infty\) functional calculus
• Uniformly elliptic operators with measurable coefficients
• Semigroup kernels, Poisson bounds, and holomorphic functional calculus
• Sharp maximal functions associated with approximations of the identity in spaces of homogeneous type and applications

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