Geodesic
$L^p$-boundedness for pseudodifferential operators with non-smooth symbols and applications
Bollettino della Unione matematica italiana, Série 8, 8B (2005) no. 2, pp. 461-503

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

Starting from a general formulation of the characterization by dyadic crowns of Sobolev spaces, the authors give a result of $L^{p}$ continuity for pseudodifferential operators whose symbol a(x,ξ) is non smooth with respect to x and whose derivatives with respect to ξ have a decay of order ρ with $0 \rho \leq 1$. The algebra property for some classes of weighted Sobolev spaces is proved and an application to multi - quasi - elliptic semilinear equations is given. 
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     author = {Garello, Gianluca and Morando, Alessandro},
     title = {$L^p$-boundedness for pseudodifferential operators with non-smooth symbols and applications},
     journal = {Bollettino della Unione matematica italiana},
     pages = {461--503},
     publisher = {mathdoc},
     volume = {Ser. 8, 8B},
     number = {2},
     year = {2005},
     zbl = {1178.35395},
     mrnumber = {MR2149396},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2005_8_8B_2_a12/}
}
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Garello, Gianluca; Morando, Alessandro. $L^p$-boundedness for pseudodifferential operators with non-smooth symbols and applications. Bollettino della Unione matematica italiana, Série 8, 8B (2005) no. 2, pp. 461-503. http://geodesic.mathdoc.fr/item/BUMI_2005_8_8B_2_a12/