Let with mean value zero, and be polynomials in variables with real coefficients and . We prove that
where may depend on , and , but not otherwise on the coefficients of and .
The above result answers an open question posed in [13]. Additional boundedness results of similar nature are also obtained.
Accepted:
Published online:
Mots-clés : oscillatory integrals, singular integrals, Calderón–Zygmund kernels, Hardy spaces
Hussain Al-Qassem 1; Leslie Cheng 2; Yibiao Pan 3

@article{CRMATH_2023__361_G10_1673_0, author = {Hussain Al-Qassem and Leslie Cheng and Yibiao Pan}, title = {On the boundedness of a family of oscillatory singular integrals}, journal = {Comptes Rendus. Math\'ematique}, pages = {1673--1681}, publisher = {Acad\'emie des sciences, Paris}, volume = {361}, year = {2023}, doi = {10.5802/crmath.523}, language = {en}, }
TY - JOUR AU - Hussain Al-Qassem AU - Leslie Cheng AU - Yibiao Pan TI - On the boundedness of a family of oscillatory singular integrals JO - Comptes Rendus. Mathématique PY - 2023 SP - 1673 EP - 1681 VL - 361 PB - Académie des sciences, Paris DO - 10.5802/crmath.523 LA - en ID - CRMATH_2023__361_G10_1673_0 ER -
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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.523/
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