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CLC number: O174.5
On-line Access: 2024-08-27
Received: 2023-10-17
Revision Accepted: 2024-05-08
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Chun-jie Zhang, Fang-fang Ren, Yu-huai Zhang, Gui-lian Gao. Boundedness of Marcinkiewicz integral with rough kernel on Triebel-Lizorkin spaces[J]. Frontiers of Information Technology & Electronic Engineering,in press.https://doi.org/10.1631/FITEE.1500082 @article{title="Boundedness of Marcinkiewicz integral with rough kernel on Triebel-Lizorkin spaces", %0 Journal Article TY - JOUR
Abstract: The paper studies the boundedness of Marcinkiewicz integral on Triebel-Lizorkin spaces, it is new and interesting in harmonic analysis.
带粗糙核的Marcinkiewicz积分在Triebel-Lizorkin空间的有界性创新点：沿用向量值奇异积分将粗糙核算子光滑化的思路，证明转后的算子具有更好的光滑性条件。 方法：首先利用本文作者之前文章的方法，把带径向粗糙项的Marckinkiewicz积分转化成研究一些具有一定光滑性的算子(需反复利用向量值奇异积分定理)。然后，利用微分指标较低时，Triebel-Lizorkin空间的一个等刻画，把Triebel-Lizorkin有界性转化成向量值的Lebesgue空间有界性。于是我们只需要研究这些有光滑性算子的向量值Lebesgue空间有界性，这整套方法是作者之前系列文章的一个整体思路。本文也利用这套思路，在该框架下，研究转化后算子的核，得到关于这个核的更精细估计，从而推广了原有结果。 结论：对于带有径向粗糙项的算子，同样可以得到一般的Marcinkiewicz积分在Triebel-Lizorkin空间的有界性。 关键词组：
Reference[1]Al-Qassem, H.M., Cheng, L.C., Pan, Y., 2012. Boundedness of rough integral operators on Triebel-Lizorkin spaces. Publ. Mat., 56(2):261-277.  [2]Chen, D.N., Chen, J.C., Fan, D.S., 2005. Rough singular integral operators on Hardy-Sobolev spaces. Appl. Math. J. Chin. Univ., 20(1):1-9. [3]Chen, J.C., Zhang, C.J., 2008. Boundedness of rough singular integral operators on the Triebel-Lizorkin spaces. J. Math. Anal. Appl., 337(2):1048-1052. [4]Chen, J.C., Fan, D.S., Ying, Y.M., 2002. Singular integral operators on function spaces. J. Math. Anal. Appl., 276(2):691-708. [5]Chen, J.C., Fan, D.S., Ying, Y.M., 2003. Certain operators with rough singular kernels. Can. J. Math., 55(3): 504-532. [6]Chen, J.C., Jia, H.Y., Jiang, L.Y., 2005. Boundedness of rough oscillatory singular integral on Triebel-Lizorkin spaces. J. Math. Anal. Appl., 306(2):385-397. [7]Chen, Q.L., Zhang, Z.F., 2004. Boundedness of a class of super singular integral operators and the associated commutators. Sci. China Ser. A, 47(6):842-853. [8]Chen, Y.P., Ding, Y., 2008. Rough singular integrals on Triebel-Lizorkin space and Besov space. J. Math. Anal. Appl., 347(2):493-501. [9]Chen, Y.P., Zhu, K., 2014. Lp bounds for the commutators of oscillatory singular integrals with rough kernels. Abs. Appl. Anal., 2014:393147.1-393147.8. [10]Zhang, C.J., Chen, J.C., 2009. Boundedness of g-functions on Triebel-Lizorkin spaces. Taiwan. J. Math., 13(3):973-981. [11]Zhang, C.J., Chen, J.C., 2010a. Boundedness of singular integrals and maximal singular integrals on Triebel-Lizorkin spaces. Int. J. Math., 21(2):157-168. [12]Zhang, C.J., Chen, J.C., 2010b. Boundedness of Marcinkiewicz integral on Triebel-Lizorkin spaces. Appl. Math. J. Chin. Univ., 25(1):48-54. [13]Zhang, C.J., Zhang, Y.D., 2013. Boundedness of oscillatory singular integral with rough kernels on Triebel-Lizorkin spaces. Appl. Math. J. Chin. Univ., 28(1):90-100. Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou
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