分数次极大交换子在分层Lie群中的有界性
Boundedness of Fractional Maximal Commutator in Stratified Lie Groups
DOI: 10.12677/PM.2022.1212238, PDF,    科研立项经费支持
作者: 田晓娇：牡丹江师范学院数学系，黑龙江 牡丹江
关键词: 分数次极大算子；交换子；广义Morrey空间；Lipschitz空间；分层Lie群；Fractional Maximal Operator； Commutator； Generalized Morrey Space； Lipschitz Space； Stratified Lie Group
摘要: 本文借助于广义Morrey空间的相关的理论与工具，在分层Lie群中考虑了由Lipschitz函数和分数次极大算子Mα生成的交换子Mα,b、[b,Mα]在广义Morrey空间中的有界性。
Abstract: In this paper, the main aim is to consider the boundedness of commutator Mα,b and [b,Mα] generated by Lipschitz function b and the fractional maximal operator Mα on stratified Lie group G with the help of relevant theories and tools of Generalized Morrey space.
文章引用：田晓娇. 分数次极大交换子在分层Lie群中的有界性[J]. 理论数学, 2022, 12(12): 2209-2216. https://doi.org/10.12677/PM.2022.1212238

参考文献

[1] Lu, S., Wu, Q. and Yang, D. (2002) Boundedness of Commutators on Hardy Type Spaces. Science in China Series A: Mathematics, 45, 984-997. [Google Scholar] [CrossRef] 
[2] Lu, S.Z. and Xu, L.F. (2006) Boundedness of Some Marcinkiewicz Integral Operators Related to Higher Order Commutators on Hardy Spaces. Acta Mathematica Sinica, 22, 105-114. [Google Scholar] [CrossRef] 
[3] Liu, Y. and Hu, Z. (2007) Boundedness for Iterated Commutators on the Mixed Norm Spaces. Journal of Mathematical Analysis and Applications, 332, 787-797. [Google Scholar] [CrossRef] 
[4] Wu, J. (2009) Boundedness of Commutators on Homogeneous Morrey-Herz Spaces over Locally Compact Vilenkin Groups. Analysis in Theory and Applications, 25, 283-296. [Google Scholar] [CrossRef] 
[5] Morrey, C.B. (1938) On the Solutions of Quasi-Linear Elliptic Partial Differential Equations. Transactions of the American Mathematical Society, 43, 126-166. [Google Scholar] [CrossRef] 
[6] Mizuhara, T. (1991) Boundedness of Some Classical Operators on Generalized Morrey Spaces. In: ICM-90 Satellite Conference Proceedings, Springer, Tokyo, 183-189. [Google Scholar] [CrossRef] 
[7] Coifman, R.R., Rochberg, R. and Weiss, G. (1976) Factorization Theorems for Hardy Spaces in Several Variables. Annals of Mathematics, 103, 611-635. [Google Scholar] [CrossRef] 
[8] Janson, S. (1978) Mean Oscillation and Commutators of Singular Integral Operators. Arkiv for Matematik, 16, 263-270. [Google Scholar] [CrossRef] 
[9] Paluszyński, M. (1995) Characterization of the Besov Spaces via the Commutator Operator of Coifman, Rochberg and Weiss. Indiana University Mathematics Journal, 44, 1-17. https://www.jstor.org/stable/24898462 [Google Scholar] [CrossRef] 
[10] Zhang, P. (2017) Characterization of Lipschitz Spaces via Commutators of the Hardy-Littlewood Maximal Function. Comptes Rendus Mathematique, 355, 336-344. [Google Scholar] [CrossRef] 
[11] Burenkov, V.I., Gogatishvili, A., Guliyev, V.S., et al. (2010) Boundedness of the Fractional Maximal Operator in Local Morrey-Type Spaces. Complex Variables and Elliptic Equations, 55, 739-758. [Google Scholar] [CrossRef] 
[12] Guliyev, V., Ekincioglu, I., Kaya, E., et al. (2019) Characterizations for the Fractional Maximal Commutator Operator in Generalized Morrey Spaces on Carnot Group. Integral Transforms and Special Functions, 30, 453-470. [Google Scholar] [CrossRef] 
[13] Guliyev, V., Akbulut, A. and Mammadov, Y. (2013) Boundedness of Fractional Maximal Operator and Their Higher Order Commutators in Generalized Morrey Spaces on Carnot Groups. Acta Mathematica Scientia, 33, 1329-1346. [Google Scholar] [CrossRef] 
[14] 常娇娇. 极大交换子在分层Lie群中的有界性[J]. 理论数学, 2022, 12(1): 80-87. [Google Scholar] [CrossRef] 
[15] Stein, E.M. and Murphy, T.S. (1993) Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals. Princeton University Press, Princeton. [Google Scholar] [CrossRef] 
[16] Folland, G.B. and Stein, E.M. (2020) Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28. Princeton University Press, Princeton. [Google Scholar] [CrossRef] 
[17] Hu, G. (2019) Littlewood-Paley Characterization of Ho ̈lder-Zygmund Spaces on Stratified Lie Groups. Czechoslovak Mathematical Journal, 69, 131-159. [Google Scholar] [CrossRef] 
[18] Wu, J.L. (2022) Characterization of Lipschitz Functions via the Commutators of the Fractional Maximal Function on Stratified Lie Groups.
[19] Nakai, E. (2006) The Campanato, Morrey and Holder Spaces on Spaces of Homogeneous Type. Studia Mathematica, 1, 1-19. [Google Scholar] [CrossRef] 

为你推荐