Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4592219 | Journal of Functional Analysis | 2006 | 44 Pages |
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.