Weighted norm inequalities, off-diagonal estimates and elliptic operators
By P. Auscher, J. M. Martell. 2008
64 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/6add0e844ae7741bfbb788caa501afb113b73aac
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In Applied Mathematics
- P. Auscher
- J. M. Martell
- Tuomas Hytönen
- A. Mcintosh
- Z. Nieraeth
- S. Hofmann
- Pierre Portal
- D. Cruz-Uribe
Citations in the corpus
- Quantitative estimates and extrapolation for multilinear weight classes (2018, methodology): “As a point of comparison, we note here that, for finite pj , our condition ~w ∈ A~p,(~r,s) is equivalent to the condition (wp11 , . . . , w pm m ) ∈ A~p,(r1,...,rm,s′), where the latter condition considers the weight class of Li, Martell, and Ombrosi defined in (1.2).”
- Weighted norm inequalities, off-diagonal estimates and elliptic operators. Part I: General operator theory and weights (2006, methodology): “In Part IV, [ AM4 ], we apply our general theory to the Riesz transform on some”
- Kato's square root problem in Banach spaces (2007, background): “by P. Auscher and J. M. Martell [ 6 ], these results are extended to a more general setting, allowing weighted estimates on spaces of homogeneous type.”
- Maximal inequalities and Riesz transform estimates on $L^p$ spaces for Schr\ (2006, unknown): “The main sledge hammer is the following criterion for Lp boundedness ([ AM1 ]).”