Weighted norm inequalities, off-diagonal estimates and elliptic operators Part II: Off-diagonal estimates on spaces of homogeneous type
By P. Auscher, J. M. Martell. 2006
80 citations recorded by the source corpus.
Abstract.This is the second part of a series of four articles on weighted norm inequalities, off-diagonal estimates and elliptic operators. We consider a substitute to the notion of pointwise bounds for kernels of operators which usually is a measure of decay. This substitute is that of off-diagonal estimates expressed in terms of local and scale invariant Lp − Lq estimates. We propose a definition in spaces of homogeneous type that is stable under composition. It is particularly well suited to semigroups. We study the case of semigroups generated by elliptic operators.
Subfields: Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/a41e1641d3aa937cf9008f75500ac991c035f40c
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In Applied Mathematics
- P. Auscher
- J. M. Martell
- S. Hofmann
- D. Cruz-Uribe
- Andrei K. Lerner
- A. Mcintosh
- Dachun Yang
- Xuan Thinh Duong
Citations in the corpus
- Weighted norm inequalities, off-diagonal estimates and elliptic operators. Part I: General operator theory and weights (2006, background): “This is a general introduction for this article and the series [ AM2 , AM3, AM4].”
- Gaussian heat kernel upper bounds via the Phragmén–Lindelöf theorem (2006, unknown): “For interesting considerations about L p − L q Gaussian estimates, see also [ 5 ].”
- Sharp weighted norm estimates beyond Calderón–Zygmund theory (2015, unknown): “By [Auscher and Martell 2007a, Theorem 3.13], T also satisfies some weighted estimates: for every p 2 . p 0 ; q 0 / and every weight !”