θ-型 Calderón-Zygmund 算子交换子在齐次变指标 Herz 空间中的有界性
Boundedness of Commutators for θ-TypeCalder′on-Zygmund Operators on Homogeneous Herz Spaces with Variable Exponents
DOI: 10.12677/PM.2023.1310293, PDF, 下载: 111  浏览: 171  科研立项经费支持
作者: 薛凤字:牡丹江师范学院数学系,牡丹江 黑龙江
关键词: θ-型 Calderón-Zygmund 算子交换子变指标 Herz 空间BMO 空间θ-Type Calder′on-Zygmund Operators Commutator Herz Spaces with Variable Exponents BMO Space
摘要: 本文研究了θ-型 Calderón-Zygmund 算子与 BMO 函数生成的交换子在具有三个变指标的齐次Herz 空间上的有界性。
Abstract: In this paper, we investigated the boundedness of commutators generated by 𝜃-type Calder´on-Zygmund operators with symbol function 𝑏 in BMO spaces on homogeneous Herz spaces with three variable exponents.
文章引用:薛凤字. θ-型 Calderón-Zygmund 算子交换子在齐次变指标 Herz 空间中的有界性[J]. 理论数学, 2023, 13(10): 2862-2876. https://doi.org/10.12677/PM.2023.1310293

参考文献

[1] Yabuta, K. (1985) Generalizations of Calderon-Zygmund Operators. Studia Mathematica, 82, 17-31.
https://doi.org/10.4064/sm-82-1-17-31
[2] 彭立中.广义Calderon-Zygmund算子及其加权模不等式[J].数学进展,1985,14(2): 97-115.
[3] Liu, Z.G. and Lu, S.Z. (2002) Endpoint Estimates for Commutators of Calderon-Zygmund Type Operators. Kodai Mathematical Journal, 25, 79-88.
https://doi.org/10.2996/kmj/1106171078
[4] 张璞,徐罕.Calderon-Zygmund型算子交换子的加权尖锐估计[J].数学学报(中文版),2005. 48(4): 625-636.
[5] Wang, H. (2016) Boundedness of 𝜃-Type Calderon-Zygmund Operators and Commutators in the Generalized Weighted Morrey Spaces. Journal of Function Spaces, 2016, Article ID: 1309348.
[6] 孙杰,张璞.θ-型Calderon-Zygmund算子交换子的端点加权估计[J].数学的实践与认识.2020. 50(1): 258-264.
[7] Acerbi, E. and Mingione, G. (2002) Regularity Results for Stationary Electro-Rheological Fluids. Archive for Rational Mechanics and Analysis, 164, 213-259.
https://doi.org/10.1007/s00205-002-0208-7
[8] Acerbi, E. and Mingione, G. (2007) Gradient Estimates for a Class of Parabolic Systems. Duke Mathematical Journal, 136, 285-230.
https://doi.org/10.1215/S0012-7094-07-13623-8
[9] Diening, L. and Ruzicka, M. (2003) Calderon-Zygmund Operators on Generalized Lebesgue Spaces 𝐿𝑝(·) and Problems Related to Fluid Dynamics. Journal fur die Reine und Angewandte Mathematik, 563, 197-220.
https://doi.org/10.1515/crll.2003.081
[10] Diening, L., Harjulehto, P., Hasto, P. and Ruzicka, M. (2011) Lebesgue and Sobolev Spaces with Variable Exponents. Springer, Berlin.
[11] Herz, C.S. (1968) Lipschitz Spaces and Bernstein's Theorem on Absolutely Convergent Fourier Transforms. Journal of Mathematics and Mechanics, 18, 283-323.
https://doi.org/10.1512/iumj.1969.18.18024
[12] Lu, S., Yang, D. and Hu, G. (2008) Herz Type Spaces and Their Applications. Science Press, Beijing.
[13] Izuki, M. (2009) Herz and Amalgam Spaces with Variable Exponent, the Haar Wavelets and Greediness of the Wavelet System. East Journal on Approximations, 15, 87-110.
[14] Almeida, A. and Drihem, D. (2012) Maximal, Potential and Singular Type Operators on Herz Spaces with Variable Exponents. Journal of Mathematical Analysis and Applications, 394, 781-795.
https://doi.org/10.1016/j.jmaa.2012.04.043
[15] Izuki, M. and Noi, T. (2011) Boundedness of Some Integral Operators and Commutators on Generalized Herz Spaces with Variable Exponents. OCAMI Preprint Series, 11.
[16] Yang, Y. and Tao, S. (2018) 𝜃-Type Calderon-Zygmund Operators and Commutators in Variable Exponents Herz Space. Open Mathematics, 16, 1607-1620.
https://doi.org/10.1515/math-2018-0133
[17] 杨沿奇,陶双平.θ型C-Z算子在加权变指数Morrey空间上的有界性[J].数学学报(中文版),2019. 62(3): 503-514.
[18] Yang, Y. and Tao, S. (2020) 𝜃-Type Calderon-Zygmund Operators on Morrey and Morrey-Herz-Type Hardy Spaces with Variable Exponents. University Politehnica of Bucharest Scientific Bulletin-Series A—Applied Mathematics and Physics, 82, 35-44.
[19] Yu, X. and Liu, Z. (2021) Boundedness of Some Integral Operators and Commutators on Homogeneous Herz Spaces with Three Variable Exponents. Frontiers of Mathematics in China, 16, 211-237.
https://doi.org/10.1007/s11464-021-0897-6
[20] Kovacik, O. and Rakosnik, J. (1991) On Spaces 𝐿𝑝(𝑥) and 𝑤𝑘,𝑝(𝑥). Czechoslovak Mathematical Journal, 41, 592-618.
https://doi.org/10.21136/CMJ.1991.102493
[21] Izuki, M. (2010) Boundedness of Commutators on Herz Spaces with Variable Exponent. Rendiconti del Circolo Matematico di Palermo, 59, 199-213.
https://doi.org/10.1007/s12215-010-0015-1
[22] Wang, L. and Tao, S. (2016) Parameterized Littlewood-Paley Operators and Their Commutators on Herz Spaces with Variable Exponents. Turkish Journal of Mathematics, 40, 122-145.
https://doi.org/10.3906/mat-1412-52
[23] Lu, G. and Zhang, P. (2014) Multilinear Calderon-Zygmund Operators with Kernels of Dini's Type and Applications. Nonlinear Analysis: Theory, Methods & Applications, 107, 92-117.
https://doi.org/10.1016/j.na.2014.05.005