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(.,.) is non smooth with respect to the first variable and whose derivatives with respect to the second one have a decay of order less than 1. The algebra property for some classes of weighted Sobolev spaces is proved and an application to multi - quasi - elliptic semilinear equations is given.
L^p boundedness for pseudodifferential operators with non smooth symbols and applications
GARELLO, Gianluca;
2005-01-01
Abstract
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(.,.) is non smooth with respect to the first variable and whose derivatives with respect to the second one have a decay of order less than 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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