Weighted norm inequalities, off-diagonal estimates and elliptic operators. Part III: Harmonic analysis of elliptic operators |
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Authors: | Pascal Auscher |
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Affiliation: | a Université de Paris-Sud et CNRS UMR 8628, 91405 Orsay cedex, France b Instituto de Matemáticas y Física Fundamental, Consejo Superior de Investigaciones Científicas, C/Serrano 123, 28006 Madrid, Spain c Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain |
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Abstract: | This is the third part of a series of four articles on weighted norm inequalities, off-diagonal estimates and elliptic operators. For L in some class of elliptic operators, we study weighted norm Lp inequalities for singular “non-integral” operators arising from L; those are the operators φ(L) for bounded holomorphic functions φ, the Riesz transforms ∇L−1/2 (or (−Δ)1/2L−1/2) and its inverse L1/2(−Δ)−1/2, some quadratic functionals gL and GL of Littlewood-Paley-Stein type and also some vector-valued inequalities such as the ones involved for maximal Lp-regularity. For each, we obtain sharp or nearly sharp ranges of p using the general theory for boundedness of Part I and the off-diagonal estimates of Part II. We also obtain commutator results with BMO functions. |
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Keywords: | Muckenhoupt weights Elliptic operators in divergence form Singular non-integral operators Holomorphic functional calculi Square functions Square roots of elliptic operators Riesz transforms Maximal regularity Commutators with bounded mean oscillation functions |
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