Morrey空间上Marcinkiewicz积分与R
Commutators of Marcinkiewicz Integrals with RBMO(μ) on Morrey Spaces
本文建立了 Marcinkiewicz 积分M与具离散系数的正则有界平均振荡空间RBMO(μ)生成的交换子Mb在非齐性度量测度空间上的有界性. 在控制函数λ满足∈-弱反双倍条件的假设下, 当p∈(1,∞)时,证明了Mb在Lp(μ)上是有界的. 另外,还得到了Mb在 Morrey 空间上的有界性.
This paper establishes the boundedness of the commutator Mb generated by the Marcinkiewicz integral M and the regularized bounded mean oscillation space with the discrete coefficient RBMO(μ) over non-homogeneous metric measure space. Under the assumption that the dominating function λ satisfies the ∈-weak reverse doubling condition, when p ∈ (1,∞), the authors prove that the Mb is bounded on the Lebesgue space Lp(μ). Furthermore, the boundedness of the Mb on the Morrey space is also obtained.
非齐性度量测度空间 / Marcinkiewicz积分 / 交换子 / RBMO(μ)空间 / Morrey空间 {{custom_keyword}} /
non-homogeneous metric measure space / Marcinkiewicz integral / commutator / RBMO(μ)space / Morrey space {{custom_keyword}} /
[1] Bui T. A., Duong X. T., Hardy spaces, regularized BMO spaces and the boundedness of Calderón–Zygmund operators on non-homogeneous spaces, J. Geom. Anal., 2013, 23: 895–932.
[2] Coifman R. R., Weiss G., Analyse Harmonique Non-commutative sur certains Espaces Homogènes, Lecture Notes in Mathematics, 242, Springer-Verlag, Berlin-New York, 1971.
[3] Coifman R. R., Weiss G., Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc., 1977, 83(4): 569–645.
[4] Cao Y. H., Zhou J., Morrey spaces for non-homogeneous metric measure spaces, Abstract and Applied Analysis, 2013, 2013(1): 1–8.
[5] Cao Y. H., Zhou J., The boundedness of Marcinkiewicz integrals commutators on non-homogeneous metric measure spaces, J. Ineq. Appl., 2015, 2015(1): 1–18.
[6] Fu X., Lin H. B., Yang D. C., Yang D. Y., Hardy spaces Hp over non-homogeneous metric measure spaces and their applications, Sci. China Math., 2015, 58(2): 309–388.
[7] Fu X., Yang D. C., Yang D. Y., The molecular characterization of the Hardy space H1 on non-homogeneous metric measure spaces and its application, J. Math. Anal. Appl., 2014, 410(2): 1028–1042.
[8] Fu X., Yang D. C., Yuan W., Generalized fractional integral and their commutators over non-homogeneous metric measure spaces, Taiwan. J. Math., 2014, 18(2): 509–557.
[9] Hytönen T., A framework for non-homogeneous analysis on metric spaces, and RBMO space of Tolsa, Publ. Math., 2010, 54(2): 485–504.
[10] Hu G. E., Lin H. B., Yang D. C., Marcinkiewicz integrals with non-doubling measures, Inte. Equ. Oper. The., 2007, 58(2): 205–238.
[11] Hytönen T., Yang D. C., Yang D. Y., The Hardy space H1 on non-homogeneous metric spaces, Math. Proc. Cambridge Philos. Soc., 2012, 153(1): 9–31.
[12] Lu G. H., Tao S. P., Generalized Morrey space over non-homogeneous metric measure spaces, J. Aus. Math. Soc., 2017, 103(2): 268–278.
[13] Lu G. H., Tao S. P., Commutators of Littlewood–Paley gκ*-functions on non-homogeneous metric measure spaces, Open Math., 2017, 15(2): 1283–1299.
[14] Lu G. H., Tao S. P., Boundedness of commutators of Marcinkiewicz integrals on non-homogeneous metric measure spaces, J. Funct. Spaces, 2015, 2015(1): 1–12.
[15] Lin H. B., Wu S. Q., Yang D. C., Boundedness of certain commutators over non-homogeneous metric measure spaces, Anal. Math. Phys., 2017, 7(2): 187–218.
[16] Lin H. B., Yang D. C., Equivalent boundedness of Marcinkiewicz integrals on non-homogeneous metric measure spaces, Sci. China Math., 2014, 57(1): 123–144.
[17] Lu G. H., Zhou J., Estimates for fractional type Marcinkiewicz integrals with non-doubling measures, J. Ine. Appl., 2014, 2014(1): 1–14.
[18] Sawano Y., Tanaka H., Morrey sapces for non-doubling measures, Acta Math. Sin., Engl. Ser., 2005, 21(6): 1535–1544.
[19] Tolsa X., Littlewood–Paley theory and the T (1) theorem with non-doubling measures, Advances in Math., 2001, 164(1): 57–116.
[20] Tolsa X., BMO, H1 and Calderón–Zygmund operators for non-doubling measures, Math. Ann., 2001, 319(1): 89–149.
[21] Wang M. M., Ma S. X., Lu G. H., Littlewood–Paley gλ,μ*-function and its commutator on non-homogeneous generalized Morrey spaces, Tokyo J. Math., in Published.
国家自然科学基金资助项目(11561062);博士科研启动基金资助项目(0002020203)
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