JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2018, Vol. 53 ›› Issue (6): 38-43.doi: 10.6040/j.issn.1671-9352.0.2017.646

Previous Articles     Next Articles

Boundedness of Marcinkiewicz integrals operators with variable kernels on Herz-type Hardy spaces with variable exponent

XIN Yin-ping1, TAO Shuang-ping2   

  1. 1. School of Information Engineering, Lanzhou University of Finance and Economics, Lanzhou 730010, Gansu, China;
    2. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Received:2017-12-19 Online:2018-06-20 Published:2018-06-13

Abstract: Based on the boundedness of Marcinkiewicz integrals on variable Lebesgue spaces and the atomic decomposition of Herz-type Hardy spaces with variable exponent, we obtain the boundedness of Marcinkiewicz integrals with variable kernels on the homogeneous and non-homogeneous Herz-type Hardy spaces with variable exponent.

Key words: Herz-type Hardy space, variable exponent, Marcinkiewicz integrals operator

CLC Number: 

  • O174.2
[1] IZUKI M. Boundedness of sublinear operators on Herz spaces with variable exponent and application to waveiet charactization[J]. Analysis Mathematica, 2010, 36(36):33-50.
[2] WANG Hongbin,LIU Zongguang. The Herz type Hardy spaces with variable exponent and their application[J]. Taiwannese Journal of Mathematics, 2012, 16(4):1363-1389.
[3] KOVÁCIK O, RÁKOSNÍK J. On spaces Lp(x) and Wk,p(x)[J]. Czechoslovak Mathematical Journal, 1991, 41(4):592-618.
[4] MUCKENHOUPT B,WHEEDEN R L. Weighted norm inequalities for singualar and fractional integrals[J]. Transactions of the American Mathematical Society, 1971, 161:249-258.
[5] NAKAI E, SAWANO Y. Hardy spaces with variable exponents and generalized Campanato spaces[J]. Journal of Functional Analysis, 2012, 262(9):3665-3748.
[6] ZYGMUND A. On singular integral with variable kernels[J]. Applicable Analysis,1978, 7(3):221-238.
[7] SAKAMOTO M, YABUTA K. Boundedness of marcinkieicz functions[J]. Studia Math, 1999, 135:103-142.
[8] DING Yong, LU Shanzhen, SHAO Shuanglin. Integral operators with varlable kernels on weak Hardy spaces[J]. Journal of Mathematical Analysis Applications, 2006, 317(1):127-135.
[9] 陶双平, 辛银萍. 带变量核的参数型 Littlewood-Paley算子在Hardy空间上的有界性[J]. 山东大学学报(理学版), 2010, 45(12):49-56. TAO Shuangping, XIN Yinping. Boundedness of Littlewood-Paley operators with variable kernels on Hardy spaces[J].Journal of Shandong University(Natural Science), 2010, 45(12):49-56.
[10] 张璞,陈杰诚. 一类带有变量核的积分算子在Herz型Hardy空间的有界性[J]. 数学年刊, 2005, 25A(5):561-570. ZHANG Pu, CHEN Jiecheng. A class of integral operators with variable kernels on the Herz-type hardy spaces[J]. Chinese Annals of Mathematics, 2005, 25A(5):561-570.
[11] 陈杰诚, 丁勇, 范大山. 带变量核的Littlewood-Paley算子[J]. 中国科学(A辑), 2006, 36(1):38-51. CHEN Jiecheng, DING Yong, FAN Dashan. Littlewood-Paley operators with variable kernels[J]. Science in China(Series A), 2006, 36(1):38-51.
[12] XUE Qingying, YABUTA K. L2-Boundedness of Marcinkiewicz Integrals along surfaces with variable kernels[J]. Sci Math Japonicae, 2006, 63(3):369-382.
[1] ZHANG Shen-gui. Multiple solutions of Navier boundary value problem for fourth-order elliptic equation with variable exponents [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(2): 32-37.
[2] ZHAO Huan, ZHOU Jiang. Commutators of multilinear Calderón-Zygmund operator on Herz-type Hardy spaces with variable exponent [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(10): 42-50.
[3] LU Qiang-de, TAO Shuang-ping. Boundedness of commutators of Calderón-Zygmund operators and fractional integrals in homogeneous grand variable exponent Lebesgue spaces [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(9): 54-58.
[4] MA Xiao-jie, ZHAO Kai. Boundedness of commutators of the fractional Hardy operators on weighted spaces with variable exponent [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(11): 106-110.
[5] WANG Jie, QU Meng, SHU Li-sheng. Boundedness of the Littlewood-Paley operators and cummutators on the Herz spaces with variable exponents [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(4): 9-18.
[6] WANG Jin-ping, ZHAO Kai. Lipschitz commutators of fractional integrals on Herz-type spaces with variable exponents [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(10): 6-10.
[7] GOU Yin-xia, TAO Shuang-ping, DAI Hui-ping. Weighted estimates of fractional integral with rough kernel and its commutators on Herz-type Hardy Spaces [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(07): 80-87.
[8] ZHOU Shu-juan, LIU Su-ying. Boundedness of linear operators on the anisotropic #br# weighted Herz-type Hardy spaces [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(04): 74-78.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!