JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2014, Vol. 49 ›› Issue (07): 80-87.doi: 10.6040/j.issn.1671-9352.0.2013.577

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Weighted estimates of fractional integral with rough kernel and its commutators on Herz-type Hardy Spaces

GOU Yin-xia, TAO Shuang-ping, DAI Hui-ping   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Received:2013-11-20 Online:2014-07-20 Published:2014-09-15

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Abstract: The main goal of this paper is to study the weighted estimates about the fractional integrals with rough kernels and its commutators on the Herz-type Hardy spaces. As Ω∈Ls(Sn-1)(1< s <∞), it is proved that the fractional integrals TΩ,l and its commutators [b,TΩ,l] generated by the BMO functions are bounded from the weighted Herz-type Hardy spaces to the weighted Herz spaces by using the atomic decompositions. Also, the corresponding results are also obtained for the maximal fractional integrals with rough kernels.

Key words: the weighted Herz-type Hardy spaces, fractional integrals, commutator, rough kernel

CLC Number: 

  • O174.2
[1] MUCKENHOUPT B, WHEEDEN R. Weighted norm inequalities for fractional integrals[J]. Trans Amer Math Soc, 1974, 192:261-274.
[2] SEGOVIA C, TORREA J L. Weight inequalities for commutators of fractional and singular integral[J]. Publ Aat, 1991, 35:209-235.
[3] SEGOVIA C, TORREA J L. Higher order commutators for Vector-Valued Calderon-Zygmund operators[J]. Trans Amer Math Soc, 1993, 336:537-556.
[4] DING Yong, LU Shanzhen. Weighted norm inequalities for fractional intrgral operators with rough kernel[J]. Canad J Math, 1998, 50(1):29-39.
[5] DING Yong, LU Shanzhen. Higher order commutators for a class of rough operators[J]. Ark Mat, 1999, 37:33-44.
[6] DING Yong. Weak type bounds for a class of rough operators with power weights[J]. Proc Amer Math Soc, 1997, 125:2939-2942.
[7] 王华. 具有粗糙核的分数次积分算子在加权Morrey空间上的有界性[J].数学学报, 2013, 56(2):176-186. WANG Hua. Boundedness of fractional integral operators with rough kernels on weighted Morrey spaces[J]. Acta Mathematic Sinice, 2013, 56(2):176-186.
[8] BEURLING A.Constructoin and analysis of some convolutional gebras[J]. Ann Inst Fourier Grenoble, 1964, 14:1-32.
[9] 陆善镇, 杨大春. 加权Herz型Hardy空间及其应用[J]. 中国科学:A辑, 1995, 38(3):235-245. LU Shanzhen, YANG Dachun. Weighted Herz-type Hardy spaces and its application[J]. Science in China: Ser A, 1995, 38(3):235-245.
[10] LU Shanzhen, YANG Dachun. The decomposition of the weighted Herz spaces on Rn and its application[J]. Science in China: Ser A, 1995, 38:147-158.
[11] LU Shanzhen, YANG Dachun. The continuity of commutators on Herz-type spaces[J]. Michigan Math, 1997, 44(2):255-280.
[12] WU Huoxiong. Boundness of higher order commutators for a class of rough operators on weighted Herz spaces[J]. Journal of Beijing Normal University: Natual Science, 2001, 37(3):299-306.
[13] 刘宗光, 曾岳生. 齐型空间上的Herz空间及其应用[J]. 数学物理学报, 1999, 19(3):270-277. LIU Zongguang, ZENG Yuesheng. The Herz spaces on spaces of homogeneous type and their applications[J]. Acta Mathematica Scientia, 1999, 19(3):270-277.
[14] 赵凯, 纪春静, 黄智. 一类Marcinkiewicz积分交换子在Herz型Hardy空间中的有界性[J]. 山东大学学报:理学版, 2013, 48(6):1-5. ZHAO Kai, JI Chunjing, HUANG Zhi. Boundedness of commutators for a class of Marcinkiewicz integral operators on Herz-type Hardy space[J]. Journal of Shandong University: Natual Science, 2013, 48(6):1-5.
[15] 陶双平, 武江龙. 齐次Morrey-Herz空间上粗糙核高阶交换子的有界性[J]. 数学进展, 2007, 36(5):607-616. TAO Shuangping, WU Jianglong. Boundedness of the higher order commutatorson the homogeneous Morrey-Herz space[J]. Advances in Mathematics, 2007, 36(5):607-616.
[16] TAO Shuangping, WU Jianglong. Boundedness of the commutators of fractional integral operators on the homogeneous Morrey-Herz spaces[J]. J of Math Res And Exp, 2007, 27(3):505-512.
[17] SUN Aiwen, SHU Lisheng. Boundedness of commutators of generalized fractional intrgral operators on the weighted Herz-type Hardy spaces[J]. Anal Theory Appl, 2010, 26(2):101-109.
[18] MUCKENHOUPT B, WHEEDEN R. Weighted bounded mean oscillation and the Hilbert transform[J]. Studia Mathematica, 1976, 54(3):221-237.
[19] JOURNE J L. Calderon-Zygmund operators, pseudo-differential operators and the cauchy integral of calderon[M]// Lecture Notes in Math, 994. New York: Springer-Verlag, 1983.
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