Weighted norm inequalities, off-diagonal estimates and elliptic operators. Part III: Harmonic analysis of elliptic operators

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 $L^p$ inequalities for singular 'non-integral' operators arising from $L$ ; those are the operators $\varphi (L)$ for bounded holomorphic functions $\varphi$, the Riesz transforms $\nabla L^{-1/2}$ (or $(-\Delta {)}^{1/2}{L}^{-1/2}$) and its inverse $L^{1/2}(-\Delta {)}^{-1/2}$, some quadratic functionals $g\_L$ and $G\_L$ of Littlewood-Paley-Stein type and also some vector-valued inequalities such as the ones involved for maximal $L^p$-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.

38 pages. Third of 4 papers

References in corpus (1)

• Weighted norm inequalities, off-diagonal estimates and elliptic operators. Part I: General operator theory and weights

Cited by in corpus (20)

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• Weighted $L^p$ Estimates of Kato Square Roots Associated to Degenerate Elliptic Operators
• The regularity problem for uniformly elliptic operators in weighted spaces
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