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Pure Mathematics 2024
变指数中心Morrey空间上的分数次积分多线性交换子
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Abstract:
该文借助分数次积分在变指数Lebesgue空间的有界性，通过应用函数的分层分解和实变技巧，得到了由分数次积分和λ-中心BMO函数生成的多线性交换子在变指数中心Morrey空间上的有界性。
With the help of the boundedness of the fractionalintegral operator on Lebesgue space with variable exponent, by applying hierarchical decomposition of function and real variable techniques, the boundedness of multilinear commutators generated by fractional singular integrals and withλ-central BMO symbols is obtained on central Morrey spaces with variable exponent.
| [1] | Stein, E.M. (1970) Singular Integrals and Differentiability Properties of Functions. Princeton University Press, Princeton. https://doi.org/10.1515/9781400883882 |
| [2] | Coifman, R.R. and Meyer, Y. (1975) On Commutators of Singular Integrals and Bilinear Singular Integrals. Transactions of the American Mathematical Society, 212, 315-331. https://doi.org/10.1090/S0002-9947-1975-0380244-8 |
| [3] | Coifmann, R. and Meyer, Y. (1978) Au delà des opérateurs pseudo-différentiels. Astérisque. |
| [4] | Kenig, C.E. and Stein, E.M. (1999) Multilinear Estimates and Fractional Integration. Mathematical Research Letters, 6, 1-15. https://doi.org/10.4310/MRL.1999.v6.n1.a1 |
| [5] | Ková？ik, O. and Rákosnik, J. (1991) On Spaces and . Czechoslovak Mathematical Journal, 41, 592-618. https://doi.org/10.21136/CMJ.1991.102493 |
| [6] | Diening, L. (2004) Maximal Function on Generalized Lebesgue Spaces . Mathematical Inequalities & Applications, 7, 245-253. https://doi.org/10.7153/mia-07-27 |
| [7] | Diening, L. (2004) Riesz Potential and Sobolev Embeddings on Generalized Lebesgueand Sobolev Spaces and . Mathematische Nachrichten, 268, 31-43. https://doi.org/10.1002/mana.200310157 |
| [8] | Cruz-Uribe, D., Fiorenza, A., Martell, J.M., et al. (2006) The Boundedness of Classical Operators on Variable Lp Spaces. Annales Fennici Mathematici, 31, 239-264. |
| [9] | Morrey, C.B. (1938) On the Solutions of Quasilinear Elliptic Partial Differential Equations. Transactuons of the American Mathematical Society, 43, 126-166. https://doi.org/10.1090/S0002-9947-1938-1501936-8 |
| [10] | Chiarenza, F. and Frasca, M. (1987) Morrey Spaces and Hardy-Littlewood Maximal Function. Rendiconti Lincei-Matematica e Applicazioni, 7, 273-297. |
| [11] | Komori, Y. and Shirai, S. (2009) Weighted Morrey Spaces and Singular Integral Operators. Mathematische Nachrichten, 282, 219-231. https://doi.org/10.1002/mana.200610733 |
| [12] | Alvarez, J., Lakey, J. and Guzmán-Partida, M. (2000) Spaces of Bounded Lambda-Central Mean Oscillation, Morrey Spaces, and Lambda-Central Carleson Measures. Collectanea Mathematica, 51, 1-47. |
| [13] | Lu, S.Z. and Yang, D.C. (1995) The Central BMO Spaces and Littlewood-Paley Operators. Approximation Theory and Its Applications, 11, 72-94. https://doi.org/10.1007/BF02836580 |
| [14] | Fan, D.S., Lu, S.Z. and Yang, D.C. (1996) Boundedness of Operators in Morrey Spaces on Homogeneous Spaces and Its Applications. Acta Mathematica Sinica, 42, 625-634. |
| [15] | Fu, Z.W., Lin, Y. and Lu, S.Z. (2008)-Central BMO Estimates for Commutators of Singular Integral Operators with Rough Kernels. Acta Mathematica Applicatae Sinica, 24, 373-386. https://doi.org/10.1007/s10114-007-1020-y |
| [16] | Tao, X.X. and Shi, Y.L. (2011) Multilinear Commutators of Calderón-Zygmund Operator on-Central Morrey Spaces. Advances in Mathematics (China), 40, 47-59. |
| [17] | Mizuta, Y., Ohno, T. and Shimomura, T. (2015) Boundedness of Maximal Operators and Sobolev’s Theorem for Non-Homogeneous Central Morrey Spaces of Variable Exponent. Hokkaido Mathematical Journal, 44, 185-201. https://doi.org/10.14492/hokmj/1470053290 |
| [18] | 陶双平, 杨雨荷. 分数次极大算子及交换子在-中心Morrey空间上的加权估计[J]. 山东大学学报(理学版), 2019, 54(8): 68-75. |
| [19] | Yu, X. and Tao, X.X. (2013) Boundedness for a Class of Generalized Commutators on-Central Morrey Spaces. Acta Mathematica Sinica, English Series, 29, 1917-1926. https://doi.org/10.1007/s10114-013-2174-4 |
| [20] | Yu, X., Zhang, H.H. and Zhao, G.P. (2016) Weighted Boundedness of Some Integral Operators on Weighted-Central Morrey Spaces. Canadian Journal of Mathematics, 31, 331-342. https://doi.org/10.1007/s11766-016-3348-5 |
| [21] | Fu, Z.W., Lu, S.Z., Wang, H.B., et al.(2019) Singular Integral Operators with Rough Kernels on Central Morrey Spaces with Variable Exponent. Annales Academiae Scientiarum Fennicae Mathematica, 44, 505-522. https://doi.org/10.5186/aasfm.2019.4431 |
| [22] | Wang, H.B. and Xu, J.S. (2019) Multilinear Fractional Integral Operators on Central Morrey Spaces with Variable Exponent. Journal of Inequalities and Applications, 2019, Article No. 311. https://doi.org/10.1186/s13660-019-2264-7 |
| [23] | Wang, H.B., Xu, J.S. and Tan, J. (2020) Boundedness of Multilinear Singular Integrals on Central Morrey Spaces with Variable Exponents. Frontiers of Mathematics in China, 15, 1011-1034. https://doi.org/10.1007/s11464-020-0864-7 |
| [24] | 辛银萍. 参数型Marcinkiewicz 积分交换子在变指数Herz-Morrey空间的加权有界性[J]. 山东大学学报(理学版), 2021, 56(4): 66-75, 85. |
| [25] | Wang, D.H., Liu, Z.G., Zhou, J., et al. (2018) Central BMO Spaces with Variable Exponent. Acta Mathematica Sinica, 61, 641-650. |
| [26] | Diening, L., Harjulehto, P., H？st？, P. and R？？i？ka, M. (2011) Lebesgue and Sobolev Spaces with Variable Exponents. Springer, Heidelberg, 69-97. https://doi.org/10.1007/978-3-642-18363-8 |
| [27] | Izuki, M. (2010) Boundedness of Sublinear Operators on Herz Spaces with Variable Exponent and Application to Wavelet Characterization. Analysis Mathematica, 36, 33-50. https://doi.org/10.1007/s10476-010-0102-8 |
| [28] | Nakai, E. and Sawano, Y. (2012) Hardy Spaces with Variable Exponents and Generalized Campanato Spaces. Journal of Functional Analysis, 262, 3665-3748. https://doi.org/10.1016/j.jfa.2012.01.004 |
