Lipschitz Estimates for Multilinear Singular Integral Operators on Hardy and Herz Type Spaces

  • Lanzhe, Liu (College of Mathematics, Changsha University of Science and Technology)
  • 투고 : 2006.01.25
  • 발행 : 2007.06.23

초록

In this paper, the boundedness for some multilinear operators generated by singular integralv operators and Lipschitz functions on Hardy and Herz-type spaces are obtained.

키워드

참고문헌

  1. S. Chanillo, A note on commutators, Indiana Univ. Math. J., 31(1982), 7-16. https://doi.org/10.1512/iumj.1982.31.31002
  2. W. G. Chen, Besov estimates for a class of multilinear singular integrals, Acta Math. Sinica, 16(2000), 613-626. https://doi.org/10.1007/s101140000059
  3. J. Cohen, A sharp estimate for a multilinear singular integral on $R^{n}$, Indiana Univ. Math. J., 30(1981), 693-702. https://doi.org/10.1512/iumj.1981.30.30053
  4. J. Cohen and J. Gosselin, On multilinear singular integral operators on $R^{n}$, Studia Math., 72(1982), 199-223. https://doi.org/10.4064/sm-72-3-199-223
  5. J. Cohen and J. Gosselin, A BMO estimate for multilinear singular integral operators, Illinois J. Math., 30(1986), 445-465.
  6. R. Coifman, R. Rochberg and G. Weiss, Factorization theorems for Hardy spaces in several variables, Ann. of Math., 103(1976), 611-635. https://doi.org/10.2307/1970954
  7. Y. Ding and S. Z. Lu, Weighted boundedness for a class rough multilinear operators, Acta Math. Sinica, 3(2001), 517-526.
  8. J. Garcia-Cuerva and J. L. Rubio de Francia, Weighted norm inequalities and related topics, North-Holland Math.16, Amsterdam, 1985.
  9. J. Garcia-Cuerva and M. L. Herrero, A theory of Hardy spaces associated to the Herz spaces, Proc. London Math. Soc., 69(1994), 605-628. https://doi.org/10.1112/plms/s3-69.3.605
  10. S. Janson, Mean oscillation and commutators of singular integral operators, Ark. Math., 16(1978), 263-270. https://doi.org/10.1007/BF02386000
  11. S. Z. Lu, Q. Wu and D. C. Yang, Boundedness of commutators on Hardy type spaces, Sci.in China(ser.A), 32(2002), 232-244.
  12. S. Z. Lu and D. C. Yang, The decomposition of the weighted Herz spaces and its applications, Sci. in China (ser.A), 38(1995), 147-158.
  13. S. Z. Lu and D. C. Yang, The weighted Herz type Hardy spaces and its applications, Sci. in China(ser.A), 38(1995), 662-673.
  14. M. Paluszynski, Characterization of the Besov spaces via the commutator operator of Coifman, Rochberg and Weiss, Indiana Univ. Math. J., 44(1995), 1-17.
  15. E. M. Stein, Harmonic Analysis: real variable methods, orthogonality and oscillatory integrals, Princeton Univ. Press, Princeton NJ, 1993.