Table of Contents Author Guidelines Submit a Manuscript
Journal of Function Spaces and Applications
Volume 2013, Article ID 257537, 7 pages
http://dx.doi.org/10.1155/2013/257537
Research Article

Higher Order Commutators of Fractional Integral Operator on the Homogeneous Herz Spaces with Variable Exponent

1School of Mathematics and Physics, Anhui Polytechnic University, Wuhu 241000, China
2School of Mathematics and Computer Science, Anhui Normal University, Wuhu 241003, China

Received 28 March 2013; Accepted 20 May 2013

Academic Editor: Dachun Yang

Copyright © 2013 Liwei Wang 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. D. R. Adams, “A note on Riesz potentials,” Duke Mathematical Journal, vol. 42, no. 4, pp. 765–778, 1975. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. S. Lu and D. Yang, “Hardy-Littlewood-Sobolev theorems of fractional integration on Herz-type spaces and its applications,” Canadian Journal of Mathematics, vol. 48, no. 2, pp. 363–380, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. S. G. Shi and Z. W. Fu, “Boundedness of sublinear operators with rough kernels on weighted Morrey spaces,” Journal of Function Spaces and Applications, vol. 2013, Article ID 784983, 9 pages, 2013. View at Publisher · View at Google Scholar
  4. O. Kováčik and J. Rákosník, “On spaces Lp(x) and Wk,p(x),” Czechoslovak Mathematical Journal, vol. 41, no. 4, pp. 592–618, 1991. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. L. Diening and M. Růžička, “Calderón-Zygmund operators on generalized Lebesgue spaces Lp(·) and problems related to fluid dynamics,” Journal für die Reine und Angewandte Mathematik, vol. 563, pp. 197–220, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. C. Capone, D. Cruz-Uribe, and A. Fiorenza, “The fractional maximal operator and fractional integrals on variable Lp spaces,” Revista Mathemática Iberoamericana, vol. 23, no. 3, pp. 743–770, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. M. Izuki, “Commutators of fractional integrals on Lebesgue and Herz spaces with variable exponent,” Rendiconti del Circolo Matematico di Palermo, vol. 59, no. 3, pp. 461–472, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. L. Diening, “Riesz potential and Sobolev embeddings on generalized Lebesgue and Sobolev spaces Lp(·) and Wk,p(·),” Mathematische Nachrichten, vol. 268, pp. 31–43, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. S. Z. Lu, D. C. Yang, and G. E. Hu, Herz Type Spaces and Their Applications, Science Press, Beijing, China, 2008.
  10. 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
  11. S. Lu, Q. Wu, and D. Yang, “Boundedness of commutators on Hardy type spaces,” Science in China A, vol. 45, no. 8, pp. 984–997, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. T. Zhou, Commutators of Fractional Integrals on Spaces With Variable Exponent, Dalian Maritime University, 2012.
  13. H. B. Wang, Z. W. Fu, and Z. G. Liu, “Higher order commutators of Marcinkiewicz integrals on variable Lebesgue spaces,” Acta Mathematica Scientia A, vol. 32, no. 6, pp. 1092–1101, 2012. View at Google Scholar
  14. H. B. Wang, Function Spaces with Variable Exponent and Related Topics, China University of Mining and Technology, 2012.
  15. A. Nekvinda, “Hardy-Littlewood maximal operator on Lpx(n),” Mathematical Inequalities & Applications, vol. 7, no. 2, pp. 255–265, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. M. Izuki, “Boundedness of commutators on Herz spaces with variable exponent,” Rendiconti del Circolo Matematico di Palermo, vol. 59, no. 2, pp. 199–213, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet