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Commutateurs d'intégrales singulières et opérateurs multilinéaires

Ronald R. Coifman, Yves Meyer (1978)

Annales de l'institut Fourier

Si A est une fonction de classe 𝒞 1 à support compacte et si T est un opérateur pseudo-différentiel classique d’ordre 1, l’opérateur f T ( A f ) - A T ( f ) est borné sur L 2 . Ce résultat se généralise aux commutateurs d’ordre supérieur.

Composition of some singular Fourier integral operators and estimates for restricted X -ray transforms

Allan Greenleaf, Gunther Uhlmann (1990)

Annales de l'institut Fourier

We establish a composition calculus for Fourier integral operators associated with a class of smooth canonical relations C ( T * X 0 ) × ( T * Y 0 ) . These canonical relations, which arise naturally in integral geometry, are such that π : C T * Y is a Whitney fold and ρ : C T * X is a blow-down mapping. If A I m ( C ) , B I m ' ( C t ) , then B A I m + m ' , 0 ( Δ , Λ ) a class of pseudodifferential operators with singular symbols. From this follows L 2 boundedness of A with a loss of 1/4 derivative.

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