A criterion on weighted $L^{p}$ boundedness for rough multilinear oscillatory singular integrals
HTML articles powered by AMS MathViewer
- by Yong Ding, Shanzhen Lu and Dachun Yang PDF
- Proc. Amer. Math. Soc. 129 (2001), 1127-1136 Request permission
Abstract:
In this paper the authors give a criterion on the weighted $L^{p}$ boundedness of the multilinear oscillatory singular integral operators with rough kernels.References
- Wengu Chen and Shanzhen Lu, Weighted inequalities for multilinear oscillatory singular integrals, Hokkaido Math. J. 26 (1997), no. 1, 163–175. MR 1432545, DOI 10.14492/hokmj/1351257812
- Wengu Chen, Guoen Hu, and Shanzhen Lu, Criterion of $(L^p,L^r)$ boundedness for a class of multilinear oscillatory singular integrals, Nagoya Math. J. 149 (1998), 33–51. MR 1619575, DOI 10.1017/S0027763000006541
- Jonathan Cohen and John Gosselin, A BMO estimate for multilinear singular integrals, Illinois J. Math. 30 (1986), no. 3, 445–464. MR 850342
- Yong Ding and Shanzhen Lu, Weighted $L^p$-boundedness for higher order commutators of oscillatory singular integrals, Tohoku Math. J. (2) 48 (1996), no. 3, 437–449. MR 1404513, DOI 10.2748/tmj/1178225342
- Javier Duoandikoetxea, Weighted norm inequalities for homogeneous singular integrals, Trans. Amer. Math. Soc. 336 (1993), no. 2, 869–880. MR 1089418, DOI 10.1090/S0002-9947-1993-1089418-5
- Javier Duoandikoetxea and José L. Rubio de Francia, Maximal and singular integral operators via Fourier transform estimates, Invent. Math. 84 (1986), no. 3, 541–561. MR 837527, DOI 10.1007/BF01388746
- Dashan Fan and Yibiao Pan, Singular integral operators with rough kernels supported by subvarieties, Amer. J. Math. 119 (1997), no. 4, 799–839. MR 1465070, DOI 10.1353/ajm.1997.0024
- José García-Cuerva and José L. Rubio de Francia, Weighted norm inequalities and related topics, North-Holland Mathematics Studies, vol. 116, North-Holland Publishing Co., Amsterdam, 1985. Notas de Matemática [Mathematical Notes], 104. MR 807149
- Steve Hofmann, On certain nonstandard Calderón-Zygmund operators, Studia Math. 109 (1994), no. 2, 105–131. MR 1269771, DOI 10.4064/sm-109-2-105-131
- Douglas S. Kurtz and Richard L. Wheeden, Results on weighted norm inequalities for multipliers, Trans. Amer. Math. Soc. 255 (1979), 343–362. MR 542885, DOI 10.1090/S0002-9947-1979-0542885-8
- Shan Zhen Lu and Yan Zhang, Criterion on $L^p$-boundedness for a class of oscillatory singular integrals with rough kernels, Rev. Mat. Iberoamericana 8 (1992), no. 2, 201–219. MR 1191344, DOI 10.4171/RMI/122
- Fulvio Ricci and E. M. Stein, Harmonic analysis on nilpotent groups and singular integrals. I. Oscillatory integrals, J. Funct. Anal. 73 (1987), no. 1, 179–194. MR 890662, DOI 10.1016/0022-1236(87)90064-4
- Saunders MacLane and O. F. G. Schilling, Infinite number fields with Noether ideal theories, Amer. J. Math. 61 (1939), 771–782. MR 19, DOI 10.2307/2371335
Additional Information
- Yong Ding
- Affiliation: Department of Mathematics, Beijing Normal University, Beijing, 100875, People’s Republic of China
- MR Author ID: 213750
- Email: dingy@bnu.edu.cn
- Shanzhen Lu
- Affiliation: Department of Mathematics, Beijing Normal University, Beijing, 100875, People’s Republic of China
- Email: lusz@bnu.edu.cn
- Dachun Yang
- Affiliation: Department of Mathematics, Beijing Normal University, Beijing, 100875, People’s Republic of China
- MR Author ID: 317762
- Email: dcyang@bnu.edu.cn
- Received by editor(s): April 29, 1999
- Received by editor(s) in revised form: July 2, 1999
- Published electronically: October 20, 2000
- Additional Notes: This project was supported by NNSF and DPFIHE of China.
- Communicated by: Christopher D. Sogge
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 1127-1136
- MSC (2000): Primary 42B20, 42B99
- DOI: https://doi.org/10.1090/S0002-9939-00-05637-9
- MathSciNet review: 1709746