Table of Contents Author Guidelines Submit a Manuscript
Journal of Function Spaces
Volume 2014, Article ID 686017, 12 pages
http://dx.doi.org/10.1155/2014/686017
Research Article

On the Multilinear Singular Integrals and Commutators in the Weighted Amalgam Spaces

School of Mathematical Sciences, Xiamen University, Xiamen, Fujian 361005, China

Received 28 September 2013; Revised 5 January 2014; Accepted 5 January 2014; Published 4 May 2014

Academic Editor: Yoshihiro Sawano

Copyright © 2014 Feng Liu 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. I. Fofana, “Continuité de l'intégrale fractionnaire et espace (Lq,lp)α,” Comptes Rendus des Séances de l'Académie des Sciences I, vol. 308, no. 18, pp. 525–527, 1989. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. Y. Komori and S. Shirai, “Weighted Morrey spaces and a singular integral operator,” Mathematische Nachrichten, vol. 282, no. 2, pp. 219–231, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. T. Iida, E. Sato, Y. Sawano, and H. Tanaka, “Multilinear fractional integrals on Morrey spaces,” Acta Mathematica Sinica (English Series), vol. 28, no. 7, pp. 1375–1384, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. L. Liu, “Boundedness for multilinear singular integral operators on Morrey spaces,” Bulletin of the Malaysian Mathematical Sciences Society II, vol. 33, no. 1, pp. 93–103, 2010. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. Z. Si, “Commutator theorems for fractional integral operators on Morrey spaces,” http://arxiv.org/abs/1203.4407.
  6. H. Wang and W. Yi, “Multilinear singular and fractional integral operators on weighted Morrey spaces,” Journal of Function Spaces and Applications, vol. 2013, Article ID 735795, 11 pages, 2013. View at Publisher · View at Google Scholar
  7. A. Bonami, J. Feuto, and I. Fofana, “Norms inequalities in some subspaces of Morrey space,” http://arxiv.org/abs/1211.3565.
  8. J. Feuto, “Norm inequalities in a class of function spaces including weighted Morrey spaces,” http://arxiv.org/abs/1205.6516.
  9. J. Feuto, “Intrinsic square functions on functions spaces including weighted Morrey spaces,” http://arxiv.org/abs/1205.0129.
  10. J. Feuto, I. Fofana, and K. Koua, “Weighted norm inequalities for a maximal operator in some subspace of amalgams,” Canadian Mathematical Bulletin, vol. 53, no. 2, pp. 263–277, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. 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
  12. T. Iida, E. Sato, Y. Sawano, and H. Tanaka, “Sharp bounds for multilinear fractional integral operators on Morrey type spaces,” Positivity, vol. 16, no. 2, pp. 339–358, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. R. R. Coifman and Y. Meyer, “On commutators of singular integrals and bilinear singular integrals,” Transactions of the American Mathematical Society, vol. 212, pp. 315–331, 1975. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. R. R. Coifman and Y. Meyer, “Commutateurs d'intégrales singulières et opérateurs multilinéaires,” Annales de l'Institut Fourier, vol. 28, no. 3, pp. 177–202, 1978. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. M. Christ and J. L. Journé, “Polynomial growth estimates for multilinear singular integral operators,” Acta Mathematica, vol. 159, no. 1-2, pp. 51–80, 1987. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. C. E. Kenig and E. M. Stein, “Multilinear estimates and fractional integration,” Mathematical Research Letters, vol. 6, no. 1, pp. 1–15, 1999. View at Publisher · View at Google Scholar
  17. 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
  18. L. Grafakos and R. H. Torres, “Maximal operator and weighted norm inequalities for multilinear singular integrals,” Indiana University Mathematics Journal, vol. 51, no. 5, pp. 1261–1276, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. 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
  20. C. Pérez, G. Pradolini, R. H. Torres, and R. Trujillo-Gonzalez, “End-point estimates for iterated commutators of multilinear singular integrals,” Bulletin of the London Mathematical Society, vol. 46, no. 1, pp. 26–42, 2014. View at Publisher · View at Google Scholar
  21. C. Pérez and R. H. Torres, “Sharp maixmal function estimates for multilinear singular integrals,” Contemporary Mathematics, vol. 320, pp. 323–331, 2003. View at Google Scholar
  22. X. T. Duong and A. MacIntosh, “Singular integral operators with non-smooth kernels on irregular domains,” Revista Matemática Iberoamericana, vol. 15, no. 2, pp. 233–265, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. X. T. Duong, L. Grafakos, and L. 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
  24. X. T. Duong, R. Gong, L. Grafakos, J. Li, and L. Yan, “Maximal operator for multilinear singular integrals with non-smooth kernels,” Indiana University Mathematics Journal, vol. 58, no. 6, pp. 2517–2541, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. 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
  26. S. Chen and H. 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
  27. R. M. Gong and J. Li, “Sharp maximal function estimates for multilinear singular integrals with non-smooth kernels,” Analysis in Theory and Applications, vol. 25, no. 4, pp. 333–348, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  28. L. Grafakos, L. Liu, and D. 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
  29. J. Lian, J. Li, and H. Wu, “Multilinear commutators of BMO functions and multilinear singular integrals with non-smooth kernels,” Applied Mathematics: A Journal of Chinese Universities, vol. 26, no. 1, pp. 109–120, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet