Geodesic
Low Frequency Estimates for Long Range Perturbations in Divergence Form
Canadian journal of mathematics, Tome 63 (2011) no. 5, pp. 961-991

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DOI

We prove a uniformcontrol as $z\,\to \,0$ for the resolvent ${{(P-z)}^{-1}}$ of long range perturbations $P$ of the Euclidean Laplacian in divergence form by combining positive commutator estimates and properties of Riesz transforms. These estimates hold in dimension $d\,\ge \,3$ when $P$ is defined on ${{\mathbb{R}}^{d}}$ and in dimension $d\,\ge \,2$ when $P$ is defined outside a compact obstacle with Dirichlet boundary conditions.
DOI : 10.4153/CJM-2011-022-9
Mots-clés : 35P25, resolvent estimates, thresholds, scattering theory, Riesz transform 
Bouclet, Jean-Marc. Low Frequency Estimates for Long Range Perturbations in Divergence Form. Canadian journal of mathematics, Tome 63 (2011) no. 5, pp. 961-991. doi: 10.4153/CJM-2011-022-9
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     title = {Low {Frequency} {Estimates} for {Long} {Range} {Perturbations} in {Divergence} {Form}},
     journal = {Canadian journal of mathematics},
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     year = {2011},
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     doi = {10.4153/CJM-2011-022-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2011-022-9/}
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