单边奇异积分与Lipschitz函数生成的Cohen型交换子的变差不等式
Variation Inequalities for Cohen Type Commutator of One-Sided Singular Integral with Lipschitz Function
摘要: 本文引入了单边奇异积分与Lipschitz函数生成的Cohen型交换子的变差算子。利用单边权的外推法,建立了上述算子从加权单边Triebel-Lizorkin空间到加权Lebesgue空间的有界性。
Abstract: In this paper, we introduce ρ-variation operator of Cohen type commutator of one-sided singular integral. By the extrapolation of one-sided weights, we establish the boundedness of the above operator from weighted Lebesgue spaces to weighed one-sided Triebel-Lizorkin spaces.
文章引用：靳茄欣, 侯宪明. 单边奇异积分与Lipschitz函数生成的Cohen型交换子的变差不等式[J]. 理论数学, 2022, 12(1): 1-13. https://doi.org/10.12677/PM.2022.121001

参考文献

[1] L´epingle, D. (1976) La variation d’ordre p des semi-martingales. Zeitschrift fu¨r Wahrschein- lichkeitstheorie und Verwandte Gebiete, 36, 295-316. [Google Scholar] [CrossRef] 
[2] Bourgain, J. (1989) Pointwise Ergodic Theorems for Arithmetric Sets. Publications Math´ematiques de l’Institut des Hautes E´tudes Scientifiques, 69, 5-45. [Google Scholar] [CrossRef] 
[3] Campbell, J., Jones, R., Reinhdd, K. and Wierdl, M. (2000) Oscillation and Variation for the Hilbert Transform. Duke Mathematical Journal, 105, 59-83. [Google Scholar] [CrossRef] 
[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. [Google Scholar] [CrossRef] 
[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. [Google Scholar] [CrossRef] 
[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. [Google Scholar] [CrossRef] 
[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. [Google Scholar] [CrossRef] 
[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. [Google Scholar] [CrossRef] 
[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. [Google Scholar] [CrossRef] 
[11] Cohen, J. (1981) A Sharp Estimate for a Multilinear Singular Integral in Rn. Indiana University Mathematics Journal, 30, 693-702. [Google Scholar] [CrossRef] 
[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´ın-Reyes, F. (1997) On Weighted Inequalities for One-Sided Singular Integrals. Proceedings of the American Mathematical Society, 125, 2057-2064. [Google Scholar] [CrossRef] 
[14] Sawyer, E. (1986) Weighted Inequalities for the One-Sided Hardy-Littlewood Maximal Func- tions. Transactions of the American Mathematical Society, 297, 53-61. [Google Scholar] [CrossRef] 
[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. [Google Scholar] [CrossRef] 
[16] Ding, Y., Lu, S. and Yabuta, K. (2006) Multilinear Singular and Fractional Integrals. Acta Mathematica Sinica, English Series, 22, 347-356. [Google Scholar] [CrossRef] 
[17] Lorente, M. and Riveros, M. (2007) Two Extrapolation Theorems for Related Weighted and Applications. Mathematical Inequalities and Applications, 10, 643-660. [Google Scholar] [CrossRef] 
[18] Mac´ıas, 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. [Google Scholar] [CrossRef] 

为你推荐