与球 Banach 函数空间相关的广义 Morrey 空间上的双线性 Caldero′n-Zygumd 算子 及其交换子的有界性
Boundedness of Bilinear C - Z Operatorsand Its Commutator Generated by onGeneralized Morrey Spaces Associated with Ball Banach Function Spaces
摘要: 本文主要讨论了双线性 C−Z 算子 T 及其交换子 [b1, b2, T ] 在与球 Banach 函数空间相关的广义 Morrey 空间 Mu(X) 上的有界性. 证明了 T 从乘积空间 Mu1 (X1) × Mu2 (X2) 到空间 Mu(Y ) 有界. 进一步, 也证明了由 b1, b2 ∈ BMO(X) 和 T 生成的交换子 [b1, b2, T ] 是从乘积空间 Mu1 (X1) × Mu2 (X2) 到空间 Mu(Y ) 有界的, 其中 u = u1u2.
Abstract: In this paper, the authors mainly discuss the boundedness of bilinear C−Z operator T and its commutator [b1, b2, T ] on generalized Morrey spaces associated with ball Banach function spaces Mu(X). The authors prove bilinear C−Z operator T is bounded from product spaces Mu1 (X1) × Mu2 (X2) into spaces Mu(Y ). Further, they also prove that the commutator [b1, b2, T ] generated by b1, b2 ∈ BMO(X) and T are bounded from product spaces Mu1 (X1) × Mu2 (X2) into spaces Mu(Y ), where u = u1u2.
文章引用：李雪梅. 与球 Banach 函数空间相关的广义 Morrey 空间上的双线性 Caldero′n-Zygumd 算子 及其交换子的有界性[J]. 理论数学, 2023, 13(5): 1157-1172. https://doi.org/10.12677/PM.2023.135121

参考文献

[1] Coifman, R.R. and Meyer, Y. (1975) On Commutators of Singular Integrals and Bilinear Singular Integrals. Transactions of the AMS, 212, 315-331.[CrossRef] 
[2] Hu, G.E. and Meng, Y. (2012) Multilinear Calderon-Zygmund Operator on Products of Hardy Spaces. Acta Mathematica Sinica, English Series, 28, 281-294. [Google Scholar] [CrossRef] 
[3] Lu, Y. and Zhu, Y.P. (2014) Boundedness of Multilinear Calderon-Zygmund Singular Operators on Morrey-Herz Spaces with Variable Exponents. Acta Mathematica Sinica, 30, 1180-1194. [Google Scholar] [CrossRef] 
[4] Wang, P.W. and Liu, Z.G. (2017) Weighted Norm Inequalities for Multilinear Calderon-Zygmund Operators in Generalized Morrey Spaces. Journal of Inequalities and Applications,2017, Article No. 48. [Google Scholar] [CrossRef] [PubMed]
[5] Sawano, Y., Ho, K.-P., Yang, D. and Yang, S. (2017) Hardy Spaces for Ball Quasi-Banach Function Spaces. Dissertationes Mathematicae, 525, 1-102. [Google Scholar] [CrossRef] 
[6] Fu, Z., Lin, Y. and Lu, S. (2008) λ-Central BMO Estimates for Commutators of Singular Integral Operators with Rough Kernels. Acta Mathematica Sinica, English Series, 24, 373-386. [Google Scholar] [CrossRef] 
[7] Fu, Z., Lu, S., Wang, H. and Wang, L. (2019) Singular Integral Operators with Rough Kernels on Central Morrey Spaces with Variable Exponent. Annales Academiα Scientiarum Fennicα, 44, 505-522. [Google Scholar] [CrossRef] 
[8] Tao, J., Yang, D. and Yang, D. (2019) Boundedness and Compactness Characterizations of Cauchy Integral Commutators on Morrey Spaces. Mathematical Methods in the Applied Sciences, 42, 1631-1651. [Google Scholar] [CrossRef] 
[9] Tao, J., Yang, D. and Yang, D. (2020) Beurling-Ahlfors Commutators on Weighted Morrey Spaces and Applications to Beltrami Equations. Potential Analysis, 53, 1467-1491. [Google Scholar] [CrossRef] 
[10] Yang, M., Fu, Z. and Sun, J. (2019) Existence and Large Time Behavior to Coupled Chemotaxis-Fluid Equations in Besov-Morrey Spaces. Journal of Differential Equations, 266, 5867-5894.[CrossRef] 
[11] Ho, K.-P. (2019) Weak Type Estimates of Singular Integral Operators on Morrey-Banach Spaces. Integral Equations and Operator Theory, 91, Article No. 20. [Google Scholar] [CrossRef] 
[12] Ho, K.-P. (2021) Erdelyi-Kober Fractional Integral Operators on Ball Banach Function Spaces. Rendiconti del Seminario Matematico della Universita di Padova, 145, 93-106. [Google Scholar] [CrossRef] 
[13] Wei, M.Q. (2022) Linear Operators and Their Commutators Generated by Calderon-Zygmund Operators on Generalized Morrey Spaces Associated with Ball Banach Function Spaces. Positivity, 26, Article No. 84. [Google Scholar] [CrossRef] 
[14] Ho, K.-P. (2021) Nonlinear Commutators on Morrey-Banach Spaces. Journal of Pseudo- Differential Operators and Applications, 12, Article No. 48. [Google Scholar] [CrossRef] 
[15] Ho, K.-P. (2020) Deffnability of Singular Integral Operators on Morrey-Banach Spaces. Journal of the Mathematical Society of Japan, 72, 155-170. [Google Scholar] [CrossRef] 
[16] Wang, W. and Xu, J. (2017) Multilinear Calderon-Zygmund Operators and Their Commu- tators with BMO Functions in Variable Exponent Morrey Spaces. Frontiers of Mathematics, 12, 1235-1246.[CrossRef] 
[17] Bennett, C. and Sharpley, R.C. (1988) Interpolation of Operators. Academic Press, Cambridge.
[18] Izuki, M. and Noi, T. (2016) Boundedness of Fractional Integrals on Weighted Herz Spaces with Variable Exponent. Journal of Inequalities and Applications, 2016, Article No. 199. [Google Scholar] [CrossRef] 
[19] Guliyev, V.S. (2012) Generalized Weighted Morrey Spaces and Higher Order Commutators of Sublinear Operators. European Journal of Mathematics, 3, 33-61.
[20] Guliyev, V.S. (2013) Generalized Local Morrey Spaces and Fractional Integral Operators with Rough Kernel. Journal of Mathematical Sciences, 193, 211-227. [Google Scholar] [CrossRef] 
[21] Duoandikoetxea, J. (2001) Fourier Analysis (Translated and Revised from the 1995 Spanish Original by David Cruz-Uribe). Graduate Studies in Mathematics, Vol. 29, American Mathematical Society, Providence, RI. [Google Scholar] [CrossRef] 
[22] Janson, S. (1978) Mean Oscillation and Commutators of Singular Integral Operators. Arkiv for Matematik, 16, 263-270. [Google Scholar] [CrossRef] 

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