Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2012, Article ID 929381, 14 pages
http://dx.doi.org/10.1155/2012/929381
Research Article

Necessary and Sufficient Conditions for Boundedness of Commutators of the General Fractional Integral Operators on Weighted Morrey Spaces

1School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China
2Department of Mathematics, Shanghai University, Shanghai 200444, China

Received 20 March 2012; Revised 5 July 2012; Accepted 20 July 2012

Academic Editor: Giovanni Galdi

Copyright © 2012 Zengyan Si and Fayou Zhao. 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. X. T. Duong and L. X. Yan, β€œOn commutators of fractional integrals,” Proceedings of the American Mathematical Society, vol. 132, no. 12, pp. 3549–3557, 2004. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  2. M. Paluszyński, β€œCharacterization 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 Β· View at Google Scholar Β· View at Zentralblatt MATH
  3. S. Shirai, β€œNecessary and sufficient conditions for boundedness of commutators of fractional integral operators on classical Morrey spaces,” Hokkaido Mathematical Journal, vol. 35, no. 3, pp. 683–696, 2006. View at Google Scholar Β· View at Zentralblatt MATH
  4. H. Wang, β€œOn some commutator theorems for fractional integral operators on the weighted morrey spaces,” http://128.84.158.119/abs/1010.2638v1.
  5. Y. Komori and S. Shirai, β€œWeighted Morrey spaces and a singular integral operator,” Mathematische Nachrichten, vol. 282, no. 2, pp. 219–231, 2009. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  6. H. Wang, β€œSome estimates for the commutators of fractional integrals associated to operators with Gaussian kenerl bounds,” http://xxx.tau.ac.il/abs/1102.4380v1.
  7. J. M. Martell, β€œSharp maximal functions associated with approximations of the identity in spaces of homogeneous type and applications,” Studia Mathematica, vol. 161, no. 2, pp. 113–145, 2004. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  8. J. García-Cuerva and J. L. Rubio de Francia, Weighted Norm Inequalities and Related Topics, vol. 116 of North-Holland Mathematics Studies, North-Holland Publishing, Amsterdam, The Netherlands, 1985.
  9. E. M. Stein and T. S. Murphy, Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, vol. 43 of Monographs in Harmonic Analysis, Princeton University Press, Princeton, NJ, USA, 1993.
  10. A. Torchinsky, Real-Variable Methods in Harmonic Analysis, vol. 123, Academic Press, Orlando, Fla, USA, 1986.
  11. J. García-Cuerva, β€œWeighted Hp spaces,” Dissertations Math, vol. 162, pp. 1–63, 1979. View at Google Scholar
  12. C. Pérez, β€œEndpoint estimates for commutators of singular integral operators,” Journal of Functional Analysis, vol. 128, no. 1, pp. 163–185, 1995. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  13. S. Janson, β€œMean oscillation and commutators of singular integral operators,” Arkiv för Matematik, vol. 16, no. 2, pp. 263–270, 1978. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH