Table of Contents Author Guidelines Submit a Manuscript
Journal of Function Spaces and Applications
Volume 2013 (2013), Article ID 363916, 12 pages
http://dx.doi.org/10.1155/2013/363916
Research Article

Multiple Weighted Estimates for Vector-Valued Multilinear Singular Integrals with Non-Smooth Kernels and Its Commutators

Department of Mathematics, Jiangxi Normal University, Jiangxi 330022, China

Received 24 March 2013; Revised 14 September 2013; Accepted 21 September 2013

Academic Editor: L. E. Persson

Copyright © 2013 Dongxiang Chen et al. 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. A. K. Lerner, S. Ombrosi, C. Pérez, R. H. Torres, and R. Trujillo-González, “New maximal functions and multiple weights for the multilinear Calderón-Zygmund theory,” Advances in Mathematics, vol. 220, no. 4, pp. 1222–1264, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. S. Chen and H. X. Wu, “Multiple weighted estimates for commutators of multilinear singular integrals with non-smooth kernels,” Journal of Mathematical Analysis and Applications, vol. 396, no. 2, pp. 888–903, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. B. T. Anh and X. T. Duong, “On commutators of vector BMO functions and multilinear singular integrals with non-smooth kernels,” Journal of Mathematical Analysis and Applications, vol. 371, no. 1, pp. 80–94, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. L. Grafakos and R. H. Torres, “Multilinear Calderón-Zygmund theory,” Advances in Mathematics, vol. 165, no. 1, pp. 124–164, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. X. T. Duong, L. Grafakos, and L. X. Yan, “Multilinear operators with non-smooth kernels and commutators of singular integrals,” Transactions of the American Mathematical Society, vol. 362, no. 4, pp. 2089–2113, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. L. Tang, “Weighted estimates for vector-valued commutators of multilinear operators,” Proceedings of the Royal Society of Edinburgh A, vol. 138, no. 4, pp. 897–922, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. L. Grafakos and J. M. Martell, “Extrapolation of weighted norm inequalities for multivariable operators and applications,” The Journal of Geometric Analysis, vol. 14, no. 1, pp. 19–46, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. D. Cruz-Uribe, J. M. Martell, and C. Pérez, “Extrapolation from A weights and applications,” Journal of Functional Analysis, vol. 213, no. 2, pp. 412–439, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. C. Fefferman and E. M. Stein, “Hp spaces of several variables,” Acta Mathematica, vol. 129, no. 3-4, pp. 137–193, 1972. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. L. Grafakos, L. G. Liu, and D. C. Yang, “Multiple-weighted norm inequalities for maximal multi-linear singular integrals with non-smooth kernels,” Proceedings of the Royal Society of Edinburgh A, vol. 141, no. 4, pp. 755–775, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet