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

By P. Auscher, J. M. Martell. 2006

81 citations recorded by the source corpus.

This is the third part of a series of four articles on weighted norm in- equalities, o-diagonal estimates and elliptic operators. For L in some class of elliptic operators, we study weighted norm L p inequalities for singular "non-integral" opera- tors arising from L ; those are the operators '(L) for bounded holomorphic functions ', the Riesz transforms rL 1/2 (or ( ) 1/2 L 1/2 ) and its inverse L 1/2 ( ) 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 L p -regularity. For each, we obtain sharp or nearly sharp ranges of p using the general theory for bound- edness of Part I and the o-diagonal estimates of Part II. We also obtain commutator results with BMO functions.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/65361b11193a30a9e40f454e87cd5deacf010574

Citations in the corpus

• Weighted norm inequalities, off-diagonal estimates and elliptic operators Part II: Off-diagonal estimates on spaces of homogeneous type (2006, unknown): “Eventually, it is operational for proving weighted estimates in [ AM3 ], which was the main motivation for developing this material.”
• Sharp weighted norm estimates beyond Calderón–Zygmund theory (2015, unknown): “See also [Auscher and Martell 2006].”