Comptes Rendus
Harmonic analysis
On the boundedness of a family of oscillatory singular integrals
Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1673-1681.

Let ΩH 1 (𝕊 n-1 ) with mean value zero, P and Q be polynomials in n variables with real coefficients and Q(0)=0. We prove that

p.v. n e i(P(x)+1/Q(x)) Ω(x/|x|) |x| n d xAΩ H 1 (𝕊 n-1 )

where A may depend on n, deg(P) and deg(Q), but not otherwise on the coefficients of P and Q.

The above result answers an open question posed in [13]. Additional boundedness results of similar nature are also obtained.

Published online:
DOI: 10.5802/crmath.523
Classification: 42B20, 42B30, 42B35
Keywords: oscillatory integrals, singular integrals, Calderón–Zygmund kernels, Hardy spaces

Hussain Al-Qassem 1; Leslie Cheng 2; Yibiao Pan 3

1 Mathematics Program, Department of Mathematics, Statistics and Physics, College of Arts and Sciences, Qatar University, 2713, Doha, Qatar
2 Department of Mathematics, Bryn Mawr College, Bryn Mawr, PA 19010, U.S.A.
3 Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, U.S.A.
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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     title = {On the boundedness of a family of oscillatory singular integrals},
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Hussain Al-Qassem; Leslie Cheng; Yibiao Pan. On the boundedness of a family of oscillatory singular integrals. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1673-1681. doi : 10.5802/crmath.523.

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