Table of Contents Author Guidelines Submit a Manuscript
International Journal of Mathematics and Mathematical Sciences
Volume 2014 (2014), Article ID 738125, 15 pages
http://dx.doi.org/10.1155/2014/738125
Research Article

Vector-Valued Inequalities in the Morrey Type Spaces

College of Mathematics and Econometrics, Hunan University, Changsha 410082, China

Received 8 February 2014; Accepted 3 May 2014; Published 15 May 2014

Academic Editor: Ingo Witt

Copyright © 2014 Hua Wang. 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. C. Fefferman and E. M. Stein, “Some maximal inequalities,” American Journal of Mathematics, vol. 93, pp. 107–115, 1971. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. J. García-Cuerva and J. L. Rubio de Francia, Weighted Norm Inequalities and Related Topics, vol. 116, North-Holland, Amsterdam, The Netherlands, 1985. View at MathSciNet
  3. B. Muckenhoupt, “Weighted norm inequalities for the Hardy maximal function,” Transactions of the American Mathematical Society, vol. 165, pp. 207–226, 1972. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. K. F. Andersen and R. T. John, “Weighted inequalities for vector-valued maximal functions and singular integrals,” Studia Mathematica, vol. 69, no. 1, pp. 19–31, 1980. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. C. L. Wu, “A characterization of some weighted inequalities for the vector-valued weighted maximal function,” Acta Mathematica Sinica, vol. 26, no. 11, pp. 2191–2198, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. C. Pérez and R. Trujillo-González, “Sharp weighted estimates for vector-valued singular integral operators and commutators,” The Tohoku Mathematical Journal, vol. 55, no. 1, pp. 109–129, 2003. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. J. L. Rubio de Francia, F. J. Ruiz, and J. L. Torrea, “Calderón-Zygmund theory for operator-valued kernels,” Advances in Mathematics, vol. 62, no. 1, pp. 7–48, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. A. Benedek, A. P. Calderón, and R. Panzone, “Convolution operators on Banach space valued functions,” Proceedings of the National Academy of Sciences of the United States of America, vol. 48, pp. 356–365, 1962. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. C. B. Morrey Jr., “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 Zentralblatt MATH · View at MathSciNet
  10. 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
  11. 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 Zentralblatt MATH · View at MathSciNet
  12. J. Peetre, “On the theory of Lp,λ spaces,” Journal of Functional Analysis, vol. 4, no. 1, pp. 71–87, 1969. View at Publisher · View at Google Scholar
  13. T. Mizuhara, “Boundedness of some classical operators on generalized Morrey spaces,” in Harmonic Analysis, ICM-90 Satellite Conference Proceedings, pp. 183–189, Springer, 1991. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. V. S. Guliyev, “Boundedness of the maximal, potential and singular operators in the generalized Morrey spaces,” Journal of Inequalities and Applications, vol. 2009, Article ID 503948, 20 pages, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. V. S. Guliyev, S. S. Aliyev, and T. Karaman, “Boundedness of a class of sublinear operators and their commutators on generalized Morrey spaces,” Abstract and Applied Analysis, vol. 2011, Article ID 356041, 18 pages, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. V. S. Guliyev, S. S. Aliyev, T. Karaman, and P. S. Shukurov, “Boundedness of sublinear operators and commutators on generalized Morrey spaces,” Integral Equations and Operator Theory, vol. 71, no. 3, pp. 327–355, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. S. Lu, D. Yang, and Z. Zhou, “Sublinear operators with rough kernel on generalized Morrey spaces,” Hokkaido Mathematical Journal, vol. 27, no. 1, pp. 219–232, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. E. Nakai, “Hardy-Littlewood maximal operator, singular integral operators and the Riesz potentials on generalized Morrey spaces,” Mathematische Nachrichten, vol. 166, pp. 95–103, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. 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 Zentralblatt MATH · View at MathSciNet
  20. D. Cruz-Uribe and C. Pérez, “Two weight extrapolation via the maximal operator,” Journal of Functional Analysis, vol. 174, no. 1, pp. 1–17, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. C. Pérez, “Sharp weighted inequalities for the vector-valued maximal function,” Transactions of the American Mathematical Society, vol. 352, no. 7, pp. 3265–3288, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet