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
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