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Pure Mathematics 2022
单边奇异积分与Lipschitz函数生成的Cohen型交换子的变差不等式
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Abstract:
[1] | L′epingle, D. (1976) La variation d’ordre p des semi-martingales. Zeitschrift fu¨r Wahrschein- lichkeitstheorie und Verwandte Gebiete, 36, 295-316. https://doi.org/10.1007/BF00532696 |
[2] | Bourgain, J. (1989) Pointwise Ergodic Theorems for Arithmetric Sets. Publications Math′ematiques de l’Institut des Hautes E′tudes Scientifiques, 69, 5-45. https://doi.org/10.1007/BF02698838 |
[3] | Campbell, J., Jones, R., Reinhdd, K. and Wierdl, M. (2000) Oscillation and Variation for the Hilbert Transform. Duke Mathematical Journal, 105, 59-83.
https://doi.org/10.1215/S0012-7094-00-10513-3 |
[4] | Campbell, J., Jones, R., Reinhdd, K. and Wierdl, M. (2003) Oscillation and Variation for Singular Integrals in Higher Dimensions. Transactions of the American Mathematical Society, 355, 2115-2137. https://doi.org/10.1090/S0002-9947-02-03189-6 |
[5] | Ding, Y., Hong, G. and Liu, H. (2017) Jump and Variational Inequalities for Rough Operators.
Journal of Fourier Analysis and Applications, 23, 679-711. https://doi.org/10.1007/s00041-016-9484-8 |
[6] | Liu, F. and Wu, H. (2015) A Criterion on Oscillation and Variation for the Commutators of Singular Integral Operators. Forum Mathematicum, 27, 77-97. https://doi.org/10.1515/forum-2012-0019 |
[7] | Liu, F., Jhang, S., Oh, S. and Fu, Z. (2019) Variation Inequalities for One-Sided Singular Integrals and Related Commutators. Mathematics, 7, Article 876. https://doi.org/10.3390/math7100876 |
[8] | Fu, Z. and Lin, Y. (2011) Weighted Boundedness for Commutators of One-Sided Operators.
Acta Mathematica Sinica, Chinese Series, 54, 705-714. |
[9] | Zhang, J. and Wu, H. (2015) Oscillation and Variation Inequalities for the Commutators of Singular Integrals with Lipschitz Functions. Journal of Inequalities and Applications, 2015,
Article No. 214. https://doi.org/10.1186/1029-242X-2015-1 |
[10] | Zhang, X. and Hou, X. (2014) Lipschitz Estimates for One-Sided Cohen’s Commutators on Weighted One-Sided Triebel-Lizorkin Spaces. Journal of Function Spaces, 2014, Article ID: 720875. https://doi.org/10.1155/2014/720875 |
[11] | Cohen, J. (1981) A Sharp Estimate for a Multilinear Singular Integral in Rn. Indiana University Mathematics Journal, 30, 693-702. https://doi.org/10.1512/iumj.1981.30.30053 |
[12] | Chen, W. and Lu, S. (2000) On Multilinear Singular Integrals in Rn. Advances in Mathematics (China), 29, 325-330. |
[13] | Aimar, H., Forzani, L. and Mart′?n-Reyes, F. (1997) On Weighted Inequalities for One-Sided Singular Integrals. Proceedings of the American Mathematical Society, 125, 2057-2064. https://doi.org/10.1090/S0002-9939-97-03787-8 |
[14] | Sawyer, E. (1986) Weighted Inequalities for the One-Sided Hardy-Littlewood Maximal Func- tions. Transactions of the American Mathematical Society, 297, 53-61. https://doi.org/10.1090/S0002-9947-1986-0849466-0 |
[15] | Andersen, K. and Sawyer, E. (1988) Weighted Norm Inequalities for Riemann-Liouville and Weyl Fractional Integral Operators. Transactions of the American Mathematical Society, 308, 547-557. https://doi.org/10.1090/S0002-9947-1988-0930071-4 |
[16] | Ding, Y., Lu, S. and Yabuta, K. (2006) Multilinear Singular and Fractional Integrals. Acta Mathematica Sinica, English Series, 22, 347-356. https://doi.org/10.1007/s10114-005-0662-x |
[17] | Lorente, M. and Riveros, M. (2007) Two Extrapolation Theorems for Related Weighted and Applications. Mathematical Inequalities and Applications, 10, 643-660. https://doi.org/10.7153/mia-10-60 |
[18] | Mac′?as, R. and Riveros, M. (2000) One-Sided Extrapolation at Infinity and Singular Integrals.
Proceedings of the Royal Society of Edinburgh Section A, 130, 1081-1102. https://doi.org/10.1017/S0308210500000585 |