Weighted norm inequalities, off-diagonal estimates and elliptic operators
Auscher, Pascal ; Martell, José Maria
HAL, hal-00331495 / Harvested from HAL
Text on HAL
We give an overview of the generalized Calder\'{o}n-Zygmund theory for ``non-integral'' singular operators, that is, operators without kernels bounds but appropriate off-diagonal estimates. This theory is powerful enough to obtain weighted estimates for such operators and their commutators with $\BMO$ functions. $L^p-L^q$ off-diagonal estimates when $p\le q$ play an important role and we present them. They are particularly well suited to the semigroups generated by second order elliptic operators and the range of exponents $(p,q)$ rules the $L^p$ theory for many operators constructed from the semigroup and its gradient. Such applications are summarized.
Publié le : 2008-10-17
Classification:  Calder\'{o}n-Zygmund theory,  spaces of homogeneous type,  Muckenhoupt weights,  singular non-integral operators,  commutators with $\BMO$ functions,  elliptic operators in divergence form,  holomorphic calculi,  Riesz transforms,  square functions,  Riemannian manifolds,  2000 MSC: 42B20, 42B25, 47A06, 35J15, 47A60, 58J35,  [MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA],  [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG],  [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] 
@article{hal-00331495,
     author = {Auscher, Pascal and Martell, Jos\'e Maria},
     title = {Weighted norm inequalities, off-diagonal estimates and elliptic operators},
     journal = {HAL},
     volume = {2008},
     number = {0},
     year = {2008},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00331495}
}

Auscher, Pascal; Martell, José Maria. Weighted norm inequalities, off-diagonal estimates and elliptic operators. HAL, Tome 2008 (2008) no. 0, . http://gdmltest.u-ga.fr/item/hal-00331495/