Table of Contents Author Guidelines Submit a Manuscript
Journal of Function Spaces and Applications
Volume 2013, Article ID 410305, 11 pages
http://dx.doi.org/10.1155/2013/410305
Research Article

Endpoint Estimates for Generalized Commutators of Hardy Operators on Space

1Department of Mathematics, Shangrao Normal University, Shangrao City 334001, China
2Department of Mathematics, Zhejiang University, Hangzhou City 310027, China
3School of Mathematical Science, Beijing Normal University, Beijing City 100875, China

Received 25 March 2013; Accepted 7 May 2013

Academic Editor: Dashan Fan

Copyright © 2013 Xiao Yu and Shanzhen Lu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. G. H. Hardy, “Note on a theorem of Hilbert,” Mathematische Zeitschrift, vol. 6, no. 3-4, pp. 314–317, 1920. View at Publisher · View at Google Scholar · View at MathSciNet
  2. A. Bényi and C. Oh, “Best constants for certain multilinear integral operators,” Journal of Inequalities and Applications, vol. 2006, Article ID 28582, 12 pages, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  3. A. Kufner and L.-E. Persson, Weighted Inequalities of Hardy Type, World Scientific, Singapore, 2003. View at MathSciNet
  4. M. Christ and L. Grafakos, “Best constants for two nonconvolution inequalities,” Proceedings of the American Mathematical Society, vol. 123, no. 6, pp. 1687–1693, 1995. View at Publisher · View at Google Scholar · View at MathSciNet
  5. Z.-w. Fu, Z.-g. Liu, S.-z. Lu, and H.-b. Wang, “Characterization for commutators of n-dimensional fractional Hardy operators,” Science in China A, vol. 50, no. 10, pp. 1418–1426, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  6. Z. Fu, S. Lu, and F. Y. Zhao, “Commutators of n-dimensional rough Hardy operators,” Science China Mathematics, vol. 54, no. 1, pp. 95–104, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  7. F. Zhao, Z. Fu, and S. Z. Lu, “Endpoint estimates for n-dimensional Hardy operators and their commutators,” Science China Mathematics, vol. 55, no. 10, pp. 1977–1990, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  8. J. Cohen, “A sharp estimate for a multilinear singular integral in n,” Indiana University Mathematics Journal, vol. 30, no. 5, pp. 693–702, 1981. View at Publisher · View at Google Scholar · View at MathSciNet
  9. J. Cohen and J. Gosselin, “A BMO estimate for multilinear singular integrals,” Illinois Journal of Mathematics, vol. 30, no. 3, pp. 445–464, 1986. View at Google Scholar · View at MathSciNet
  10. W. Chen and G. Hu, “Weak type H1, L1 estimate for a multilinear singular integral operator,” Advances in Mathematics, vol. 30, no. 1, pp. 63–69, 2001. View at Google Scholar · View at MathSciNet
  11. S. Lu and Q. Wu, “Endpoint estimates for certain commutators of fractional and singular integrals,” Proceedings of the American Mathematical Society, vol. 131, no. 2, pp. 467–477, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  12. D. Y. Yan, Some problems on multilinear singular integral operators and multilinear oscillatory singular integral operators [Ph.D. thesis], Beijing Normal University, Beijing, China, 2001.
  13. C. Wang and Z. Zhang, “A new proof of Wu's theorem on vortex sheets,” Science China Mathematics, vol. 55, no. 7, pp. 1449–1462, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  14. S. J. Wu, “Mathematical analysis of vortex sheets,” Communications on Pure and Applied Mathematics, vol. 59, no. 8, pp. 1065–1206, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  15. Q. Wu and D. C. Yang, “On fractional multilinear singular integrals,” Mathematische Nachrichten, vol. 239, pp. 215–235, 2002. View at Google Scholar · View at MathSciNet
  16. J. García-Cuerva and J. L. R. de Francia, Weighted Norm Inequalities and Related Topics, vol. 116, North-Holland, Amsterdam, The Netherland, 1985. View at MathSciNet
  17. B. Muckenhoupt and R. L. Wheeden, “Weighted bounded mean oscillation and the Hilbert transform,” Studia Mathematica, vol. 54, no. 3, pp. 221–237, 1976. View at Google Scholar · View at MathSciNet
  18. S. Z. Lu and F. Y. Zhao, “CBMO estimates for multilinear Hardy operators,” Acta Mathematica Sinica, vol. 26, no. 7, pp. 1245–1254, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  19. D. Yang and Y. Zhou, “A boundedness criterion via atoms for linear operators in Hardy spaces,” Constructive Approximation, vol. 29, no. 2, pp. 207–218, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  20. B. Bajsanski and R. Coifman, “On singular integrals,” in Proceedings of Symposia in Pure Mathematics, vol. 10, pp. 1–17, American Mathematical Society, Chicago, Ill, USA, 1967.