Table of Contents Author Guidelines Submit a Manuscript
Journal of Function Spaces
Volume 2017, Article ID 3690452, 10 pages
https://doi.org/10.1155/2017/3690452
Research Article

Boundedness for Commutators of Bilinear -Type Calderón-Zygmund Operators on Nonhomogeneous Metric Measure Spaces

1Department of Mathematics, Chaohu University, Hefei 238000, China
2School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, China
3Department of Mathematics, Anhui Normal University, Wuhu 241000, China

Correspondence should be addressed to Lisheng Shu; nc.ude.unha.liam@hsluhs

Received 22 September 2016; Accepted 21 November 2016; Published 9 January 2017

Academic Editor: Yoshihiro Sawano

Copyright © 2017 Rulong Xie 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. T. Hytönen, “A framework for non-homogeneous analysis on metric spaces, and the RBMO space of Tolsa,” Publicacions Matemàtiques, vol. 54, no. 2, pp. 485–504, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  2. T. Hytönen, D. Yang, and D. Yang, “The Hardy space H1 on non-homogeneous metric spaces,” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 153, no. 1, pp. 9–31, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. T. A. Bui and X. T. Duong, “Hardy spaces, regularized BMO spaces and the boundedness of Calderón-Zygmund operators on non-homogeneous spaces,” Journal of Geometric Analysis, vol. 23, no. 2, pp. 895–932, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. S. Liu, D. Yang, and D. Yang, “Boundedness of Calderón-Zygmund operators on non-homogeneous metric measure spaces: equivalent characterizations,” Journal of Mathematical Analysis and Applications, vol. 386, no. 1, pp. 258–272, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. X. Fu, D. Yang, and W. Yuan, “Boundedness of multilinear commutators of Calderón-Zygmund operators on Orlicz spaces over non-homogeneous spaces,” Taiwanese Journal of Mathematics, vol. 16, no. 6, pp. 2203–2238, 2012. View at Google Scholar · View at MathSciNet · View at Scopus
  6. X. Fu, D. Yang, and W. Yuan, “Generalized fractional integrals and their commutators over non-homogeneous metric measure spaces,” Taiwanese Journal of Mathematics, vol. 18, no. 2, pp. 509–557, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. C. Yonghui and Z. Jiang, “The boundedness of Marcinkiewicz integrals commutators on non-homogeneous metric measure spaces,” Journal of Inequalities and Applications, vol. 2015, article no. 259, 2015. View at Publisher · View at Google Scholar · View at Scopus
  8. X. Fu, H. Lin, D. Yang, and D. Yang, “Hardy spaces Hp over non-homogeneous metric measure spaces and their applications,” Science China Mathematics, vol. 58, no. 2, pp. 309–388, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. G. Hu, Y. Meng, and D. Yang, “Weighted norm inequalities for multilinear Calderón-Zygmund operators on non-homogeneous metric measure spaces,” Forum Mathematicum, vol. 26, no. 5, pp. 1289–1322, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. T. Hytönen and H. Martikainen, “Non-homogeneous Tb theorem and random dyadic cubes on metric measure spaces,” Journal of Geometric Analysis, vol. 22, no. 4, pp. 1071–1107, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. T. Hytönen, S. Liu, D. Yang, and D. Yang, “Boundedness of Calderón-Zygmund operators on non-homogeneous metric measure spaces,” Canadian Journal of Mathematics, vol. 64, no. 4, pp. 892–923, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. H. Lin, S. Wu, and D. Yang, “Boundedness of certain commutators over non-homogeneous metric measure spaces,” Analysis and Mathematical Physics, 2016. View at Publisher · View at Google Scholar
  13. S. Liu, Y. Meng, and D. Yang, “Boundedness of maximal Calderón-Zygmund operators on non-homogeneous metric measure spaces,” Proceedings of the Royal Society of Edinburgh Section A: Mathematics, vol. 144, no. 3, pp. 567–589, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. C. Tan and J. Li, “Littlewood-Paley theory on metric spaces with non doubling measures and its applications,” Science China Mathematics, vol. 58, no. 5, pp. 983–1004, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. R. Xie, H. Gong, and X. Zhou, “Commutators of multilinear singular integral operators on non-homogeneous metric measure spaces,” Taiwanese Journal of Mathematics, vol. 19, no. 3, pp. 703–723, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. K. Yabuta, “Generalization of Calderón-Zygmund operators,” Studia Mathematica, vol. 82, pp. 17–31, 1985. View at Google Scholar
  17. R. Xie and L. Shu, “Θ-type Calderón-Zygmund operators with non-doubling measures,” Acta Mathematicae Applicatae Sinica, English Series, vol. 29, no. 2, pp. 263–280, 2013. View at Publisher · View at Google Scholar
  18. C. Ri and Z. Zhang, “Boundedness of θ-type Calderón-Zygmund operators on Hardy spaces with non-doubling measures,” Journal of Inequalities and Applications, vol. 323, pp. 1–10, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. C. Ri and Z. Zhang, “Boundedness of θ-type Calderón-Zygmund operators on nonhomogeneous metric measure spaces,” Frontiers of Mathematics in China, vol. 11, no. 1, pp. 141–153, 2016. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  20. T. Zheng, X. Tao, and X. Wu, “Bilinear Calderón-Zygmund operators of type ω(t) on non-homogeneous space,” Journal of Inequalities and Applications, vol. article 113, pp. 1–18, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. T. Zheng, Z. Wang, and W. Xiao, “Maximal bilinear Calderón-Zygmund operators of type ω(t) on non-homogeneous space,” Annals of Functional Analysis, vol. 6, no. 4, pp. 134–154, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  22. H. Gong, R. Xie, and C. Xu, “Multilinear fractional integral operators on non-homogeneous metric measure spaces,” Journal of Inequalities and Applications, vol. 2016, article no. 275, 2016. View at Publisher · View at Google Scholar · View at MathSciNet
  23. H. Lin and D. Yang, “Spaces of type BLO on non-homogeneous metric measure,” Frontiers of Mathematics in China, vol. 6, no. 2, pp. 271–292, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  24. X. Tolsa, “BMO, H1, and Calderón-zygmund operators for non doubling measures,” Mathematische Annalen, vol. 319, pp. 89–101, 2001. View at Google Scholar