Table of Contents Author Guidelines Submit a Manuscript
Journal of Function Spaces
Volume 2016, Article ID 4149314, 13 pages
http://dx.doi.org/10.1155/2016/4149314
Research Article

On the Theory of Multilinear Singular Operators with Rough Kernels on the Weighted Morrey Spaces

Department of Mathematics, Zhejiang University of Science and Technology, Hangzhou 310023, China

Received 27 February 2016; Accepted 10 July 2016

Academic Editor: Shijun Zheng

Copyright © 2016 Sha He and Xiangxing Tao. 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. 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
  2. S. Hofmann, “On certain nonstandard Calderón-Zygmund operators,” Studia Mathematica, vol. 109, no. 2, pp. 105–131, 1994. View at Google Scholar · View at MathSciNet
  3. S. Z. Lu, H. X. Wu, and P. Zhang, “Multilinear singular integrals with rough kernel,” Acta Mathematica Sinica (English Series), vol. 19, no. 1, pp. 51–62, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. Y. Ding and S. Z. Lu, “Weighted boundedness for a class of rough multilinear operators,” Acta Mathematica Sinica—English Series, vol. 17, no. 3, pp. 517–526, 2001. View at Publisher · View at Google Scholar · View at MathSciNet
  5. S. Z. Lu and P. Zhang, “Lipschitz estimates for generalized commutators of fractional integrals with rough kernel,” Mathematische Nachrichten, vol. 252, no. 1, pp. 70–85, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. C. B. Morrey, “On the solutions of quasi-linear elliptic partial differential equations,” Transactions of the American Mathematical Society, vol. 43, no. 1, pp. 126–166, 1938. View at Publisher · View at Google Scholar · View at MathSciNet
  7. F. Chiarenza and M. Frasca, “Morrey spaces and Hardy-Littlewood maximal function,” Rendiconti di Matematica e delle sue Applicazioni, vol. 7, no. 3-4, pp. 273–279, 1987. View at Google Scholar · View at MathSciNet
  8. D. Fan, S. Lu, and D. Yang, “Regularity in Morrey spaces of strong solutions to nondivergence elliptic equations with VMO coefficients,” Georgian Mathematical Journal, vol. 5, no. 5, pp. 425–440, 1998. View at Publisher · View at Google Scholar · View at MathSciNet
  9. J. Peetre, “On the theory of Lρ,λ spaces,” Journal of Functional Analysis, vol. 4, no. 1, pp. 71–87, 1969. View at Publisher · View at Google Scholar · View at Scopus
  10. 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 MathSciNet · View at Scopus
  11. H. Wang, “The boundedness of some operators with rough kernel on the weighted Morrey spaces,” Acta Mathematica Sinica, vol. 55, no. 4, pp. 589–600, 2012 (Chinese). View at Google Scholar
  12. M. Paluszynski, “Characterization of the Besov spaces via the commutator operator of Coifman, Rochberg and Weiss,” Indiana University Mathematics Journal, vol. 44, no. 1, pp. 1–17, 1995. View at Publisher · View at Google Scholar · View at MathSciNet
  13. R. A. DeVore and R. C. Sharpley, “Maximal functions measuring smoothness,” Memoirs of the American Mathematical Society, vol. 47, no. 293, 1984. View at Publisher · View at Google Scholar · View at MathSciNet
  14. Y. Ding and S. Z. Lu, “Weighted norm inequalities for fractional integral operators with rough kernel,” Canadian Journal of Mathematics, vol. 50, no. 1, pp. 29–39, 1998. View at Publisher · View at Google Scholar · View at MathSciNet
  15. L. Grafakos, Modern Fourier Analysis, vol. 250 of Graduate Texts in Mathematics, Springer, New York, NY, USA, 2nd edition, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  16. S. Z. Lu, Y. Ding, and D. Y. Yan, Singular Integrals aand Related Topics, World Scientific, 2007.
  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