Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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QUANTITATIVE WEIGHTED ESTIMATES FOR OSCILLATORY SINGULAR INTEGRALS WITH ROUGH KERNELS

  • Chen, Yanping (School of Mathematics and Physics University of Science and Technology Beijing) ;
  • Tao, Wenyu (School of Mathematics and Physics University of Science and Technology Beijing)
  • Received : 2021.03.17
  • Accepted : 2021.09.09
  • Published : 2022.01.31
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Abstract

In this paper, we obtain the quantitative weighted bounds of oscillatory singular integral with rough kernel. Moreover, the quantitative weighted bounds of maximally truncated oscillatory singular integral with rough kernel are also obtained.

Keywords

Acknowledgement

This work was financially supported by National Natural Science Foundation of China (No. 11871096 and 11471033).

References

  1. H. M. Al-Qassem, L. Cheng, and Y. Pan, Rough oscillatory singular integrals on ℝn, Studia Math. 221 (2014), no. 3, 249-267. https://doi.org/10.4064/sm221-3-4
  2. S. M. Buckley, Estimates for operator norms on weighted spaces and reverse Jensen inequalities, Trans. Amer. Math. Soc. 340 (1993), no. 1, 253-272. https://doi.org/10.2307/2154555
  3. J. M. Conde-Alonso, A. Culiuc, F. Di Plinio, and Y. Ou, A sparse domination principle for rough singular integrals, Anal. PDE 10 (2017), no. 5, 1255-1284. https://doi.org/10.2140/apde.2017.10.1255
  4. D. Fan and Y. Pan, Singular integral operators with rough kernels supported by subvarieties, Amer. J. Math. 119 (1997), no. 4, 799-839. https://doi.org/10.1353/ajm.1997.0024
  5. N. Fujii, Weighted bounded mean oscillation and singular integrals, Math. Japon. 22 (1977/78), no. 5, 529-534.
  6. T. Hytonen and C. Perez, Sharp weighted bounds involving A∞, Anal. PDE 6 (2013), no. 4, 777-818. https://doi.org/10.2140/apde.2013.6.777
  7. T. P. Hytonen, L. Roncal, and O. Tapiola, Quantitative weighted estimates for rough homogeneous singular integrals, Israel J. Math. 218 (2017), no. 1, 133-164. https://doi.org/10.1007/s11856-017-1462-6
  8. B. Krause and M. T. Lacey, Sparse bounds for maximally truncated oscillatory singular integrals, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 20 (2020), no. 2, 415-435.
  9. M. T. Lacey, An elementary proof of the A2 bound, Israel J. Math. 217 (2017), no. 1, 181-195. https://doi.org/10.1007/s11856-017-1442-x
  10. A. K. Lerner, A note on weighted bounds for rough singular integrals, C. R. Math. Acad. Sci. Paris 356 (2018), no. 1, 77-80. https://doi.org/10.1016/j.crma.2017.11.016
  11. K. Li, C. Perez, I. P. Rivera-Rios, and L. Roncal, Weighted norm inequalities for rough singular integral operators, J. Geom. Anal. 29 (2019), no. 3, 2526-2564. https://doi.org/10.1007/s12220-018-0085-4
  12. S. Z. Lu and Y. Zhang, Criterion on Lp-boundedness for a class of oscillatory singular integrals with rough kernels, Rev. Mat. Iberoamericana 8 (1992), no. 2, 201-219.
  13. H. Ojanen, Weighted estimates for rough oscillatory singular integrals, J. Fourier Anal. Appl. 6 (2000), no. 4, 427-436. https://doi.org/10.1007/BF02510147
  14. F. Di Plinio, T. P. Hytonen, and K. Li, Sparse bounds for maximal rough singular integrals via the Fourier transform, Ann. Inst. Fourier (Grenoble) 70 (2020), no. 5, 1871-1902.
  15. F. 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. https://doi.org/10.1016/0022-1236(87)90064-4
  16. E. M. Stein and G. Weiss, Interpolation of operators with change of measures, Trans. Amer. Math. Soc. 87 (1958), 159-172. https://doi.org/10.2307/1993094
  17. J. M. Wilson, Weighted inequalities for the dyadic square function without dyadic A∞, Duke Math. J. 55 (1987), no. 1, 19-50. https://doi.org/10.1215/S0012-7094-87-05502-5
  18. H. Wu, Boundedness of higher order commutators of oscillatory singular integrals with rough kernels, Studia Math. 167 (2005), no. 1, 29-43. https://doi.org/10.4064/sm167-1-3