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Characterization for commutators of n-dimensional fractional Hardy operators

Science in China Series A: Mathematics volume 50, pages 1418–1426 (2007)Cite this article

Abstract

In this paper, it was proved that the commutator \(\mathcal{H}_{\beta ,b} \) generated by an n-dimensional fractional Hardy operator and a locally integrable function b is bounded from L p1 (ℝn) to L p2 (ℝn) if and only if b is a CṀO(ℝn) function, where 1/p 1 − 1/p 2 = β/n, 1 < p 1 < ∞, 0 ⩽ β < n. Furthermore, the characterization of \(\mathcal{H}_{\beta ,b} \) on the homogenous Herz space \(\dot K_q^{\alpha ,p} \)(ℝn) was obtained.

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Authors and Affiliations

  1. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China

    Zun-wei Fu & Shan-zhen Lu

  2. Department of Mathematics, Linyi Normal University, Linyi, 276005, China

    Zun-wei Fu

  3. Department of Mathematics, China University of Mining and Technology (Beijing), Beijing, 100083, China

    Zong-guang Liu & Hong-bin Wang

Authors
  1. Zun-wei Fu
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  2. Zong-guang Liu
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  3. Shan-zhen Lu
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  4. Hong-bin Wang
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Corresponding author

Correspondence to Shan-zhen Lu.

Additional information

This work was partially supported by the National Natural Science Foundation of China (Grant Nos. 10571014, 10371080) and the Doctoral Programme Foundation of Institute of Higher Education of China (Grant No. 20040027001)

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Fu, Zw., Liu, Zg., Lu, Sz. et al. Characterization for commutators of n-dimensional fractional Hardy operators. SCI CHINA SER A 50, 1418–1426 (2007). https://doi.org/10.1007/s11425-007-0094-4

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  • DOI: https://doi.org/10.1007/s11425-007-0094-4

Keywords

  • n-dimensional fractional Hardy operator
  • commutator
  • CṀO function
  • homogeneous Herz space

MSC(2000)

  • 42B20
  • 42B35