Acta Mathematica Sinica

, Volume 22, Issue 1, pp 69–76 | Cite as

Continuity for Maximal Multilinear Bochner–Riesz Operators on Hardy and Herz–Hardy Spaces



Let \( B^{A}_{{\delta , * }} \)be the maxiamal multilinear Bochner–Riesz operators generated by Bochner– Riesz operators and D α A ∈ Lipβ(|α| = m). The continuity of the operator on some Hardy and Herz type Hardy is obtained.


Bochner–Riesz operator Multilinear Operators Hardy Space Herz Space Lipschitz space 

MR (2000) Subject Classification

42B20 42B25 


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  1. 1.
    Lu, S. Z.: Four lectures on real H p spaces, World Scientific Publishing, River Edge, NI, 1995Google Scholar
  2. 2.
    Hu, G. E., Lu, S. Z., The commutator of the Bochner–Riesz operator. Tohoku Math. J., 48, 259–266 (1996)MATHMathSciNetGoogle Scholar
  3. 3.
    Liu, L. Z., The continuity of commutators on Triebel–Lizorkin spaces. Integral Equations and Operator Theory, 49, 650–75 (2004)Google Scholar
  4. 4.
    Cohen, J.: A sharp estimate for a multilinear singular integral on R n. Indiana Univ. Math. J., 30, 693–702 (1981)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Cohen, J., Gosselin, J.: On multilinear singular integral operators on R n. Studia Math., 72, 199–223 (1982)MathSciNetGoogle Scholar
  6. 6.
    Cohen, J., Gosselin, J.: A BMO estimate for multilinear singular integral operators. Illinois J. Math., 30, 445–465 (1986)MATHMathSciNetGoogle Scholar
  7. 7.
    Ding, Y., Lu, S. Z.: Weighted boundedness for a class rough multilinear operators. Acta Math. Sinica, English Series, 17, 517–526 (2001)MATHCrossRefGoogle Scholar
  8. 8.
    Chen, W. G.: A Besov estimate for a class of multilinear singular integrals. Acta Math. Sinica, English Series, 16, 613–626 (2000)MATHCrossRefGoogle Scholar
  9. 9.
    Lu, S. Z., Wu, Q., Yang, D. C.: Boundedness of commutators on Hardy type spaces. Sci. in China (Ser. A)), 45, 984–997 (2002)MATHCrossRefGoogle Scholar
  10. 10.
    Garcia-Cuerva, J., Herrero, M. J. L.: A theory of Hardy spaces associated to Herz spaces. Proc. London Math. Soc., 69, 605–628 (1994)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Lu, S. Z., Yang, D. C.: The decomposition of the weighted Herz spaces and its applications. Sci. in China (Ser. A), 38, 147–158 (1995)MATHGoogle Scholar
  12. 12.
    Lu, S. Z., Yang, D. C.: The weighted Herz type Hardy spaces and its applications. Sci. in China (Ser. A), 38, 662–673 (1995)MATHGoogle Scholar
  13. 13.
    Paluszynski, M.: Characterization of the Besov spaces via the commutator operator of Coifman, Rochberg and Weiss. Indiana Univ. Math. J., 44, 1–17 (1995)MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Stein, E. S.: Harmonic Analysis: real variable methods, orthogonality and oscillatory integrals, Princeton Univ. Press, Princeton, N. J., 1993Google Scholar
  15. 15.
    Janson, S.: Mean oscillation and commutators of singular integral operators. Ark. Math., 16, 263–270 (1978)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Department of Mathematics, ChangshaUniversity of Science and TechnologyChangsha 410077P. R. China
  2. 2.Department of MathematicsBeijing Normal UniversityBeijing 100875P. R. China

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