Approximation Theory and its Applications

, Volume 16, Issue 2, pp 80–100 | Cite as

Boundedness of generalized fractional integrals in weighted Herz-type spaces

  • Tang Canqin
  • Yang Dachun


In this paper, the authors investigate the boundedness of the generalized fractional integrals of Pérez on the weighted Herz spaces, the weighted weak Herz spaces and the weighted Herz-type Hardy spaces for general weights.


Fractional Integral General Weight Weighted Lebesgue Space Vilenkin Group Generalize Fractional Integral 


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  1. [1]
    Hu, G., Lu, S., and Yang, D., The Weak Herz Spaces, J. of Beijing Normal Univ. (Nat. Sci.), 33(1997), 27–34.MATHMathSciNetGoogle Scholar
  2. [2]
    Hu, G., Lu, S. and Yang, D., The Applications of Weak Herz Spaces, Adv. in Math. (China), 26(1997), 417–428.MATHMathSciNetGoogle Scholar
  3. [3]
    Kitada, T., Potential Operators and Multipliers on Locally Compact Vilenkin Groups, Bull. Austral. Math. Soc., 54(1996), 459–471.MATHMathSciNetCrossRefGoogle Scholar
  4. [4]
    Kitada, T. and Yang, D., Potential Operators in Weighted Herz-type Spaces over Locally Compact Vilenkin Groups, Acta Math. Hungary, to appear.Google Scholar
  5. [5]
    Liu, Z., Several Problems on Herz-type Spaces (in Chinese), Ph. D. Dissertation, Zhejiang University-Xixi Campus, Zhejiang, 1999.Google Scholar
  6. [6]
    Long, S., and Wang, J., Boundedness of Fractional Integrals on Weighted Herz Space (in Chinese), J. of Math. (PRC), 18(1998), 349–354.MATHMathSciNetGoogle Scholar
  7. [7]
    Lu, S. and Yabuta, K. and Yang, D., Boundedness of Some Sublinear Operators in Weighted Herz-type Spaces, Kodai Math. J., to appear.Google Scholar
  8. [8]
    Lu, S. and Yang, D., Hardy-Littlewood-Sobolev Theorems of Fractional Integration on Herztype Spaces and its Applications, Canad. J. of Math., 48(1996), 363–380.MATHMathSciNetGoogle Scholar
  9. [9]
    Lu, S. and Yang, D., The Decomposition of Weighted Herz Spaces on Rn and its Applications, Sci. in China (Ser. A), 38(1995), 147–158.MATHMathSciNetGoogle Scholar
  10. [10]
    Lu, S. and Yang, D., The Weighted Herz-type Hardy Spaces and its Applications, Sci. in China (Ser. A), 38(1995), 662–673.MATHMathSciNetGoogle Scholar
  11. [11]
    Muckenhoupt, B. and Weighted, R. L., Wiehgted Norm Inequalities for Fractional integrals, Trans. Amer. Math. Soc., 192(1974), 261–274.MATHCrossRefMathSciNetGoogle Scholar
  12. [12]
    Pérez, C., Two Weighted Inequalities for Potential and Fractional Type Maximal Operators, Indiana Univ Math. J., 43(1994), 663–683.MATHCrossRefMathSciNetGoogle Scholar
  13. [13]
    Pérez, C., Two Weighted Norm Inequalities for Reisz Potential and Uniform Lp-Weighted Sobolev Inequalities, Indiana Univ. Math. J., 39(1990), 31–44.MATHCrossRefMathSciNetGoogle Scholar
  14. [14]
    Stromberg, J. O. and Wheeden, R. L., Fractional Integrals on Weighted Hp and Lp Spaces, Trans. Amer. Math. Soc., 287(1985), 293–321.CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer 2000

Authors and Affiliations

  • Tang Canqin
    • 1
  • Yang Dachun
    • 1
  1. 1.Department of MathematicsBeijing Normal UniversityBeijingThe People’s Republic of China

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