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

摘要

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 phi(L) for bounded holomorphic functions phi, the Riesz transforms del L-1/2 (or (-Delta)L-1/2(-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. (c) 2006 Elsevier Inc. All rights reserved.