Marcinkiewicz积分算子及其交换子在非齐度量测度空间上的有界性

Abstract

Abstract:

Let $ ({\cal X}, d, \mu) $ be a non-homogeneous metric measure space satisfying both the geometrically doubling and the upper doubling conditions. By using the properties of non-homogeneous metric measure space and inequality technique, the authors proved that the Marcinkiewicz integral operator and its commutator are bounded on Herz spaces and Herz type Hardy spaces with non-homogeneous metric measure space.

Key words: Non-homogeneous metric measure space, Herz space, Hardy space, Marcinkiewicz integral, Boundedness

CLC Number:

O174.2

Yaoyao Han,Kai Zhao. Boundedness of Marcinkiewicz Integral and Its Commutator on Non-Homogeneous Metric Measure Spaces[J].Acta mathematica scientia,Series A, 2020, 40(3): 597-610.

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References 19

1	Coifman R R , Weiss G . Analyse Harmonique Non-Commutative sur Certains Espaces Homogénes. Berlin: Springer-Verlag, 1971
2	Tolsa X . BMO, H¹ and Calderón-Zygmund operators for non-doubling measures. Math Ann, 2001, 319 (1): 89- 149 doi: 10.1007/PL00004432
3	Hu G E , Meng Y , Yang D C . Endpoint estimate for maxmial commutators with non-doubling measures. Acta Math Sci, 2006, 26B (2): 271- 280
4	Lin H B , Meng Y , Yang D C . Weighted estimates for commutators of multilinear Calderón-Zygmund operators with non-doubling measures. Acta Math Sci, 2010, 30B (1): 1- 18
5	Yang D C , Yang D Y , Hu G E . The Hardy Space H¹ with Non-Doubling Measures and Their Application. Berlin: Springer-Verlag, 2013
6	Hytönen T . A framework for non-homogeneous analysis on metric spaces, and the RBMO space of Tolsa. Publ Mat, 2010, 54, 485- 504 doi: 10.5565/PUBLMAT_54210_10
7	Fu X , Lin H B , Yang D C , et al. Hardy spaces H^p over non-homogeneous metric measure spaces and their applications. Sci China Math, 2015, 58, 309- 388 doi: 10.1007/s11425-014-4956-2
8	韩瑶瑶, 赵凯. 非齐度量测度空间上的Herz型Hardy空间. 中国科学:数学, 2018, 48 (10): 1315- 1338
	Han Y Y , Zhao K . Herz type Hardy spaces on non-homogeneous metric measure spaces. Sci Sin Math, 2018, 48 (10): 1315- 1338
9	Stein E M . On the functions of Littlewood-Paley, Lusin and Marcinkiewicz. Trans Amer Math Soc, 1958, 88 (2): 430- 466 doi: 10.1090/S0002-9947-1958-0112932-2
10	Ding Y , Fan D S , Pan Y B . Weighted boundedness for a class of rough Marcinkiewicz integrals. Indiana Univ Math J, 1999, 48 (3): 1037- 1055
11	Chen D X , Chen J C . Boundedness of Marcinkiewicz integrals with rough kernels on Herz spaces. Adv Math (China), 2005, 34 (5): 591- 599
12	Mo H X , Lu S Z . Boundedness of generalized high commutators of Marcinkiewicz integrals. Acta Math Sci, 2007, 27B (4): 852- 866
13	程美芳, 束立生. Marcinkiewicz积分算子交换子在Hardy空间及Herz型Hardy空间上的有界性. 数学物理学报, 2008, 28A (2): 222- 231
	Cheng M F , Shu L S . Boundedness of the commutator of Marcinkiewicz integral on Hardy space and Herz-type Hardy space. Acta Math Sci, 2008, 28A (2): 222- 231
14	陶祥兴, 位瑞英. 可变核Marcinkiewicz积分交换子在Herz型Hardy空间上的有界性. 数学物理学报, 2009, 29A (6): 1508- 1517
	Tao X X , Wei R Y . Boundedness of commutators related to Marcinkiewicz integrals with variable kernels in Herz-type Hardy spaces. Acta Math Sci, 2009, 29A (6): 1508- 1517
15	王洪彬, 傅尊伟, 刘宗光. 变指标Lebesgue空间上的Marcinkiewicz积分高阶交换子. 数学物理学报, 2012, 32A (6): 1092- 1101 doi: 10.3969/j.issn.1003-3998.2012.06.009
	Wang H B , Fu Z W , Liu Z G . Higher-order commutators of Marcinkiewicz integrals on variable Lebesgue spaces. Acta Math Sci, 2012, 32A (6): 1092- 1101 doi: 10.3969/j.issn.1003-3998.2012.06.009
16	Heinonen J . Lectures on Analysis on Metric Spaces. New York: Springer-Verlag, 2001
17	Hytönen T , Yang D C , Yang D Y . The Hardy space H¹ on non-homogeneous metric spaces. Math Proc Cambridge Philos Soc, 2012, 153, 9- 31 doi: 10.1017/S0305004111000776
18	王萍.非齐度量测度空间上的几类算子[D].兰州:西北师范大学, 2016
	Wang P. Some Operators on Non-Homogeneous Metric Measure Spaces[D]. Lanzhou: Northwest Normal University, 2016
19	Lin H B , Yang D C . Equivalent boundedness of Marcinkiewicz integrals on non-homogeneous metric measure spaces. Sci China Math, 2014, 57, 123- 144 doi: 10.1007/s11425-013-4754-2

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Boundedness of Marcinkiewicz Integral and Its Commutator on Non-Homogeneous Metric Measure Spaces

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