Comptes Rendus
Analyse harmonique
A note on singular oscillatory integrals with certain rational phases
Chenyan Wang1 ; Huoxiong Wu1 
1 School of Mathematical Sciences, Xiamen University, Xiamen 361005, China
Comptes Rendus. Mathématique, Volume 361 (2023), pp. 363-370.

Let Ω be homogeneous of degree zero with mean value zero, P and Q real polynomials on ℝ n with Q(0)=0 and Ω∈B q 0,0 (S n-1 ) for some q>1. This note extends and improves a classical result of Stein and Wainger (Ann. Math. Stud. 112, pp. 307-355, (1986)) to the following general form

p.v.∫ ℝ n e i(P(x)+1/Q(x)) Ω(x/|x|) |x| n dx≤B,

where B depend only on ∥Ω∥ B q 0,0 (S n-1 ) , n and the degrees of P and Q, but not on their coefficients.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/crmath.418
Classification : 42B15, 42B20, 42A50, 42A45
Chenyan Wang 1 ; Huoxiong Wu 1

1 School of Mathematical Sciences, Xiamen University, Xiamen 361005, China
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Chenyan Wang; Huoxiong Wu. A note on singular oscillatory integrals with certain rational phases. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 363-370. doi : 10.5802/crmath.418. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.418/

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