非齐型空间上分数型Marcinkiewicz积分算子的加权估计

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非齐型空间上分数型Marcinkiewicz积分算子的加权估计林海波, 王宸雁中国农业大学理学院北京 100083 Weighted Estimates for Fractional Type Marcinkiewicz Integral Operators on Non-homogeneous Spaces Hai Bo LIN, Chen Yan WANGCollege of Science, China Agricultural University, Beijing 100083, P. R. China

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摘要令（X，d，μ）为满足所谓上倍双倍条件和几何双倍条件的度量测度空间.设M_β，ρ，q为（X，d，μ）上的分数型Marcinkiewicz积分算子.在本文中，作者证明了若β ∈[0，∞），ρ ∈（0，∞），q ∈（1，∞）且M_β，ρ，q在L²（μ）上有界，则M_β，ρ，q是从加权Lebesgue空间L^p（w）到加权弱Lebesgue空间L^p，∞（w）上有界和从加权Morrey空间L^p，κ，η（ω）到加权弱Morrey空间WL^p，κ，η（ω）上有界.

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收稿日期: 2019-08-14

MR (2010):

O177.2

基金资助:国家自然科学基金资助项目（11471042）

通讯作者:王宸雁E-mail: chenyanwangcau@126.com

作者简介: 林海波,E-mail:haibolincau@126.com

引用本文:

林海波, 王宸雁. 非齐型空间上分数型Marcinkiewicz积分算子的加权估计[J]. 数学学报, 2020, 63(5): 443-464. Hai Bo LIN, Chen Yan WANG. Weighted Estimates for Fractional Type Marcinkiewicz Integral Operators on Non-homogeneous Spaces. Acta Mathematica Sinica, Chinese Series, 2020, 63(5): 443-464.

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http://www.actamath.com/Jwk_sxxb_cn/CN/或 http://www.actamath.com/Jwk_sxxb_cn/CN/Y2020/V63/I5/443

[1] Bui T. A., Duong X. T., Hardy spaces, regularized BMO spaces and the boundedness of Marcinkiewicz 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, (French) Étude de Certaines Intégrales Singulières, Lecture Notes in Mathematics, Vol. 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, 83:569-645.
[4] Fu X., Lin H., Yang Da., et al., Hardy spaces Hp over non-homogeneous metric measure spaces and their applications, Sci. China Math., 2015, 58:309-388.
[5] Fu X., Yang Da., Yang Do., The molecular characterization of the Hardy space H¹ on non-homogeneous metric measure spaces and its application, J. Math. Anal. Appl., 2014, 410:1028-1042.
[6] Grafakos L., Modern Fourier Analysis, 2nd edition, Graduate Texts in Mathematics, Vol. 250, Springer, New York, 2009.
[7] Han Y., Müller D., Yang D., A theory of Besov and Triebel-Lizorkin spaces on metric measure spaces modeled on Carnot-Carathéodory spaces, Abstr. Appl. Anal., 2008, Art. ID 893409:1-250.
[8] Heinonen J., Lectures on Analysis on Metric Spaces, Springer-Verlag, New York, 2001.
[9] Hu G., Lin H., Yang D., Marcinkiewicz integrals with non-doubling measures, Integral Equations Operator Theory, 2007, 58:205-238.
[10] Hu G., Meng Y., Yang D., Weighted norm inequalities for multilinear Calderön-Zygmund operators on non-homogeneous metric measure spaces, Forum Math., 2014, 26:1289-1322.
[11] Hu G., Yang D., Weighted norm inequalities for maximal singular integrals with nondoubling measures, Studia Math., 2008, 187:101-123.
[12] Hytönen T., A framework for non-homogeneous analysis on metric spaces, and the RBMO space of Tolsa, Publ. Mat., 2010, 54:485-504.
[13] Hytönen T., Yang Da., Yang Do., The Hardy space H¹ on non-homogeneous metric spaces, Math. Proc. Cambridge Philos. Soc., 2012, 153:9-31.
[14] John F., Quasi-isometric mappings, in:Seminari 1962/63 Anal. Alg. Geom. e Topol. Vil. 2, Ist. Naz. Alta Mat., Ediz. Cremonese, Rome, 1965:462-473.
[15] Journé J. L., Calderón-Zygmund Operator, Pseudo-Differential Operators and the Cauchy Integral of Calderón, Lecture Notes in Mathematics, Vol. 994, Springer-Verlag, Berlin, 1983.
[16] Komori J., Weighted estimates for operators generated by maximal functions on nonhomogeneous spaces, Georgian Math. J., 2005, 12:121-130.
[17] Lerner A. K., Weighted norm inequalities for the local sharp maximal function, J. Fourier Anal. Appl., 2004, 10:465-474.
[18] Lin H., Yang D., Equivalent boundedness of Marcinkiewicz integrals on non-homogeneous metric measure spaces, Sci. China Math., 2014, 57:123-144.
[19] Lu G., Tao S., Fractional type Marcinkiewicz integrals over non-homogeneous metric measure spaces, J. Inequal. Appl., 2016, 1:259-274.
[20] Marcinkiewicz J., Surquelques intégrales du type de Dini, Ann. Soc. Polon. Math., 1938, 17:42-50.
[21] Nakamura S., Generalized weighted Morrey spaces and classical operators, Math. Nachr., 2016, 289:2235-2262.
[22] Orobitg J., Pérez C., Ap weights for nondoubling measures in Rn and applications, Trans. Amer. Math. Soc., 2002, 354:2013-2033.
[23] Sawano Y., Yabuta K., Fractional type Marcinkiewicz integral operators associated to surfaces, J. Inequal. Appl., 2014, 1:232-261.
[24] Sawano Y., Yabuta K., Weighted estimates for fractional type Marcinkiewicz integral operators associated to surfaces, In:Some Topics in Harmonic Analysis and Applications, Adv. Lect. Math., 2016, 34:331-367.
[25] Stein E. M., On the functions of Littlewood-Paley, Lusin, and Marcinkiewicz, Trans. Amer. Math. Soc., 1958, 88:430-466.
[26] Strömberg J. O., Bounded mean oscillation with Orlicz norms and duality of Hardy spaces, Indiana Univ. Math. J., 1979, 28:511-544
[27] Strömberg J. O., Torchinsky A., Weighted Hardy Spaces, Lecture Notes in Math., Vol. 1381, Springer-Verlag, Berlin, 1989.
[28] Tolsa X., BMO H¹, and Calderón-Zygmund operators for non doubling measures, Math. Ann., 2001, 319:89-149.
[29] Tolsa X., Littlewood-Paley theory and the T (1) theorem with non-doubling measures, Adv. Math., 2001, 164:57-116.
[30] Tolsa X., Painlevé's problem and the semiadditivity of analytic capacity, Acta Math., 2003, 190:105-149.
[31] Tolsa X., Analytic capacity and Calderón-Zygmund theory with non doubling measures, In:Seminar of Mathematical Analysis, 2004, 71:239-271.
[32] Wang S., Jiang Y., Li B., Weighted estimated for Marcinkiewicz integral with non-doubling measures, J. Math. Res. Appl., 2012, 32:223-234.
[33] Xue Q., Yabuta K., Yan J., Fractional type Marcinkiewicz integral operators on function spaces, Forum Math., 2015, 27(5):3079-3109.
[34] Yan Y., Chen J., Lin H., Weighted Morrey spaces on non-homogeneous metric measure spaces, J. Math. Anal. Appl., 2017, 452(1):335-350.
[35] Yang Da., Yang Do., Hu G., The Hardy Space H¹ with Non-doubling Measures and Their Applications, Lecture Notes in Math., Vol. 2084, Springer-Verlag, Berlin, 2013.

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