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International Journal of Analysis
Volume 2013, Article ID 108623, 6 pages
http://dx.doi.org/10.1155/2013/108623
Research Article

Integral Estimates for the Potential Operator on Differential Forms

Department of Mathematics, Seattle University, Seattle, WA 98122, USA

Received 2 October 2012; Accepted 21 November 2012

Academic Editor: Tohru Ozawa

Copyright © 2013 Casey Johnson and Shusen Ding. 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. R. P. Agarwal, S. Ding, and C. A. Nolder, Inequalities for Differential Forms, Springer, New York, NY, USA, 2009. View at Zentralblatt MATH · View at MathSciNet
  2. H. Bi, “Weighted inequalities for potential operators on differential forms,” Journal of Inequalities and Applications, vol. 2010, Article ID 713625, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. H. Bi and Y. Xing, “Poincaré-type inequalities with Lp(log L)α-norms for Green's operator,” Computers and Mathematics with Applications, vol. 60, no. 10, pp. 2764–2770, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  4. B. Liu, “Arλ(Ω)-weighted imbedding inequalities for A-harmonic tensors,” Journal of Mathematical Analysis and Applications, vol. 273, no. 2, pp. 667–676, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  5. Y. Wang, “Two-weight Poincaré-type inequalities for differential forms in Ls(μ)-averaging domains,” Applied Mathematics Letters, vol. 20, no. 11, pp. 1161–1166, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  6. X. Yuming, “Weighted integral inequalities for solutions of the A-harmonic equation,” Journal of Mathematical Analysis and Applications, vol. 279, no. 1, pp. 350–363, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  7. Y. Xing and Y. Wang, “Bmo and Lipschitz norm estimates for composite operators,” Potential Analysis, vol. 31, no. 4, pp. 335–344, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. Y. Xing, “A new weight class and Poincaré inequalities with the Radon measures,” Journal of Inequalities and Applications, vol. 2012, article 32, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  9. S. M. Buckley and P. Koskela, “Orlicz-hardy inequalities,” Illinois Journal of Mathematics, vol. 48, no. 3, pp. 787–802, 2004. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. S. G. Staples, “Lp-averaging domains and the Poincaré inequality,” Annales Academiæ Scientiarum Fennicæ Mathematica, vol. 14, pp. 103–127, 1989. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. S. Ding and C. A. Nolder, “Ls(μ)-averaging domains,” Journal of Mathematical Analysis and Applications, vol. 283, no. 1, pp. 85–99, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. S. Ding, “Lφ(μ)-averaging domains and the quasi-hyperbolic metric,” Computers and Mathematics with Applications, vol. 47, no. 10-11, pp. 1611–1618, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet