Morrey空间上Marcinkiewicz积分与■交换子
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摘要
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■生成的交换子M_b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M_b在L~P(μ)上是有界的.另外,还得到了M_b在Morrey空间上的有界性.
This paper establishes the boundedness of the commutator M_b generated by the Marcinkiewicz integral M and the regularized bounded mean oscillation space with the discrete coefficient ■ over non-homogeneous metric measure space.Under the assumption that the dominating function λ satisfies the e-weak reverse doubling condition, when p ∈(1,∞), the authors prove that the M_b is bounded on the Lebesgue space L~p(μ). Furthermore, the boundedness of the M_b on the Morrey space is also obtained.
This paper establishes the boundedness of the commutator M_b generated by the Marcinkiewicz integral M and the regularized bounded mean oscillation space with the discrete coefficient ■ over non-homogeneous metric measure space.Under the assumption that the dominating function λ satisfies the e-weak reverse doubling condition, when p ∈(1,∞), the authors prove that the M_b is bounded on the Lebesgue space L~p(μ). Furthermore, the boundedness of the M_b on the Morrey space is also obtained.
引文
[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 Heardy space H~1 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]Hytonen 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]Hytonen T., Yang D. C., Yang D. Y., The Hardy space H~1 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 g_k~*-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, Hl and Calder6n-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 g_(λ,μ)~*,_μ-function and its commutator on non-homogeneous generalized Morrey spaces, Tokyo J. Math., in Published.
[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 Heardy space H~1 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]Hytonen 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]Hytonen T., Yang D. C., Yang D. Y., The Hardy space H~1 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 g_k~*-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, Hl and Calder6n-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 g_(λ,μ)~*,_μ-function and its commutator on non-homogeneous generalized Morrey spaces, Tokyo J. Math., in Published.