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$L^{p}$ -boundedness for pseudodifferential operators with non-smooth symbols and applications

Gianluca Garello; Alessandro Morando — 2005

Bollettino dell'Unione Matematica Italiana

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 $0 < ρ \leq 1$ . 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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L p -boundedness for pseudodifferential operators with non-smooth symbols and applications

$L^{p}$ -boundedness for pseudodifferential operators with non-smooth symbols and applications