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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 196459, 8 pages
http://dx.doi.org/10.1155/2013/196459
Research Article

Morrey Spaces for Nonhomogeneous Metric Measure Spaces

Department of Mathematics, Xinjiang University, Urumqi 830046, China

Received 6 May 2013; Accepted 14 August 2013

Academic Editor: Vakhtang M. Kokilashvili

Copyright © 2013 Cao Yonghui and Zhou Jiang. 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. J. García-Cuerva and A. E. Gatto, “Boundedness properties of fractional integral operators associated to non-doubling measures,” Studia Mathematica, vol. 162, no. 3, pp. 245–261, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. G. Hu, Y. Meng, and D. Yang, “Multilinear commutators for fractional integrals in non-homogeneous spaces,” Publicacions Matemàtiques, vol. 48, no. 2, pp. 335–367, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. X. Tolsa, “BMO, H1, and Calderón-Zygmund operators for non doubling measures,” Mathematische Annalen, vol. 319, no. 1, pp. 89–149, 2001. View at Publisher · View at Google Scholar · View at MathSciNet
  4. X. Tolsa, “Littlewood-Paley theory and the T(1) theorem with non-doubling measures,” Advances in Mathematics, vol. 164, no. 1, pp. 57–116, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. X. Tolsa, “The space H1 for nondoubling measures in terms of a grand maximal operator,” Transactions of the American Mathematical Society, vol. 355, no. 1, pp. 315–348, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. X. Tolsa, “Painlevé's problem and the semiadditivity of analytic capacity,” Acta Mathematica, vol. 190, no. 1, pp. 105–149, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. X. Tolsa, “The semiadditivity of continuous analytic capacity and the inner boundary conjecture,” American Journal of Mathematics, vol. 126, no. 3, pp. 523–567, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. W. Chen, Y. Meng, and D. Yang, “Calderón-Zygmund operators on Hardy spaces without the doubling condition,” Proceedings of the American Mathematical Society, vol. 133, no. 9, pp. 2671–2680, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. W. Chen and E. Sawyer, “A note on commutators of fractional integrals with (u) functions,” Illinois Journal of Mathematics, vol. 46, no. 4, pp. 1287–1298, 2002. View at Zentralblatt MATH · View at MathSciNet
  10. 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 Zentralblatt MATH · View at MathSciNet
  11. 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 Zentralblatt MATH · View at MathSciNet
  12. 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 Zentralblatt MATH · View at MathSciNet
  13. J. Zhou and B. L. Ma, “Marcinkiewicz commutators with Lipschitz functions in non-homogeneous spaces,” Canadian Mathematical Bulletin, vol. 55, no. 3, pp. 646–662, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. 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 Zentralblatt MATH · View at MathSciNet
  15. H. Lin, E. Nakai, and D. Yang, “Boundedness of Lusin-area and gλ* functions on localized BMO spaces over doubling metric measure spaces,” Bulletin des Sciences Mathématiques, vol. 135, no. 1, pp. 59–88, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. H. Lin and D. Yang, “An interpolation theorem for sublinear operators on non-homogeneous metric measure spaces,” Banach Journal of Mathematical Analysis, vol. 6, no. 2, pp. 168–179, 2012. View at Zentralblatt MATH · View at MathSciNet
  17. 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 Zentralblatt MATH · View at MathSciNet
  18. Y. Sawano and H. Tanaka, “Morrey spaces for non-doubling measures,” Acta Mathematica Sinica, vol. 21, no. 6, pp. 1535–1544, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. Y. Sawano, “lq-valued extension of the fractional maximal operators for non-doubling measures via potential operators,” International Journal of Pure and Applied Mathematics, vol. 26, no. 4, pp. 505–523, 2006. View at Zentralblatt MATH · View at MathSciNet
  20. Y. Sawano and H. Tanaka, “Equivalent norms for the Morrey spaces with non-doubling measures,” Far East Journal of Mathematical Sciences, vol. 22, no. 3, pp. 387–404, 2006. View at Zentralblatt MATH · View at MathSciNet
  21. 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 Zentralblatt MATH · View at MathSciNet
  22. X. Fu, D. Yang, and W. Yuan, “Generalized fractional integrals and their commutators over non-homogeneous spaces,” 2012.
  23. H. Lin and D. Yang, “Equivalent Boundedness of Marcinkiewicz integrals on nonhomogeneous metric measure spaces,” 2012.
  24. V. S. Guliyev and Y. Sawano, “Linear and sublinear operators on Generalized Morrey spaces with non-doubling measures,” Publicationes Mathematicae Debrecen, vol. 83, no. 3, pp. 1–17, 2013.
  25. J. Heinonen, Lectures on Analysis on Metric Spaces, Springer, New York, NY, USA, 2001.
  26. G. Di Fazio and M. A. Ragusa, “Commutators and Morrey spaces,” Unione Matematica Italiana. Bollettino A, vol. 5, no. 3, pp. 323–332, 1991. View at Zentralblatt MATH · View at MathSciNet
  27. J. Peetre, “On the theory of Lpλ spaces,” Journal of Functional Analysis, vol. 4, pp. 71–87, 1969.
  28. V. Kokilashvili and A. Meskhi, “Maximal functions and potentials in variable exponent Morrey spaces with non-doubling measure,” Complex Variables and Elliptic Equations, vol. 55, no. 8–10, pp. 923–936, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  29. L. I. Hedberg, “On certain convolution inequalities,” Proceedings of the American Mathematical Society, vol. 36, pp. 505–510, 1972. View at Publisher · View at Google Scholar · View at MathSciNet
  30. D. E. Edmunds, V. Kokilashvili, and A. Meskhi, Bounded and Compact Integral Operators, chapter 6, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2002. View at MathSciNet
  31. I. Sihwaninggrum and Y. Sawano, “Weak and strong type estimates for fractional integral opertors on Morrey spaces in metric measure spaces,” Eurasian Mathematical Journal, vol. 4, no. 1, pp. 76–81, 2013.
  32. A. Eridani, V. Kokilashvili, and A. Meskhi, “Morrey spaces and fractional integral operators,” Expositiones Mathematicae, vol. 27, no. 3, pp. 227–239, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  33. 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