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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 829218, 9 pages
http://dx.doi.org/10.1155/2013/829218
Research Article

Estimates of Some Operators on One-Sided Weighted Morrey Spaces

Department of Mathematics, Linyi University, Linyi 276005, China

Received 13 August 2013; Revised 30 September 2013; Accepted 3 October 2013

Academic Editor: Bashir Ahmad

Copyright © 2013 Shaoguang Shi and Zunwei Fu. 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. F. J. Martín-Reyes, P. Ortega Salvador, and A. de la Torre, “Weights for one-sided operators,” in Recent Development in Real and Harmonic Analysis, Applied and Numerical Harmonic Analysis, Birkhäuser, Boston, Mass, USA, 2009.
  2. P. Butzer and U. Westphal, “Introduction to fractional calculus,” in Fractional Calculus, Applications in Physics, H. Hilfer, Ed., pp. 1–85, World Scientific, Singapore, 2000.
  3. Z. W. Fu, S. Z. Lu, and W. Yuan, “A weighted variant of Riemann-Liouville fractional integrals on n,” Abstract and Applied Analysis, vol. 2012, Article ID 780132, 18 pages, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  4. E. Sawyer, “Weighted inequalities for the one-sided Hardy-Littlewood maximal functions,” Transactions of the American Mathematical Society, vol. 297, no. 1, pp. 53–61, 1986. View at Publisher · View at Google Scholar · View at MathSciNet
  5. H. Aimar, L. Forzani, and F. J. Martín-Reyes, “On weighted inequalities for singular integrals,” Proceedings of the American Mathematical Society, vol. 125, no. 7, pp. 2057–2064, 1997. View at Publisher · View at Google Scholar · View at MathSciNet
  6. K. F. Andersen and E. T. Sawyer, “Weighted norm inequalities for the Riemann-Liouville and Weyl fractional integral operators,” Transactions of the American Mathematical Society, vol. 308, no. 2, pp. 547–558, 1988. View at Publisher · View at Google Scholar · View at MathSciNet
  7. Z. Fu, S. Lu, S. Sato, and S. Shi, “On weighted weak type norm inequalities for one-sided oscillatory singular integrals,” Studia Mathematica, vol. 207, no. 2, pp. 137–151, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  8. F. J. Martín-Reyes, P. Ortega Salvador, and A. de la Torre, “Weighted inequalities for one-sided maximal functions,” Transactions of the American Mathematical Society, vol. 319, no. 2, pp. 517–534, 1990. View at Publisher · View at Google Scholar · View at MathSciNet
  9. F. J. Martín-Reyes and A. de la Torre, “One-sided BMO spaces,” Journal of the London Mathematical Society, vol. 49, no. 3, pp. 529–542, 1994. View at Publisher · View at Google Scholar · View at MathSciNet
  10. F. J. Martín-Reyes and A. de la Torre, “Two weight norm inequalities for fractional one-sided maximal operators,” Proceedings of the American Mathematical Society, vol. 117, no. 2, pp. 483–489, 1993. View at Publisher · View at Google Scholar · View at MathSciNet
  11. H. Aimar and R. Crescimbeni, “On one-sided BMO and Lipschitz functions,” Annali della Scuola Normale Superiore di Pisa Serie IV, vol. 27, no. 3-4, pp. 437–456, 1998. View at MathSciNet
  12. Z. W. Fu and S. Z. Lu, “One-sided Triebel-Lizorkin space and its applications,” Scientia Sinica Mathematica, vol. 41, pp. 43–52, 2011.
  13. S. Ombrosi and L. de Rosa, “Boundedness of the Weyl fractional integral on one-sided weighted Lebesgue and Lipschitz spaces,” Publicacions Matemàtiques, vol. 47, no. 1, pp. 71–102, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  14. L. de Rosa and C. Segovia, “Equivalence of norms in one-sided Hp spaces,” Collectanea Mathematica, vol. 53, no. 1, pp. 1–20, 2002. View at MathSciNet
  15. P. G. Lemarié-Rieusset, “The Navier-Stokes equations in the critical Morrey-Campanato space,” Revista Matemática Iberoamericana, vol. 23, no. 3, pp. 897–930, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  16. G. Lu, “Embedding theorems on Campanato-Morrey spaces for vector fields and applications,” Comptes Rendus de l'Académie des Sciences. Série I., vol. 320, no. 4, pp. 429–434, 1995. View at MathSciNet
  17. G. Lu, “Embedding theorems on Campanato-Morrey spaces for vector fields on Hörmander type,” Approximation Theory and Its Applications, vol. 14, no. 1, pp. 69–80, 1998. View at MathSciNet
  18. H. Triebel, Theory of Function Spaces. II, vol. 84 of Monographs in Mathematics, Birkhäuser, Basel, Switzerland, 1992. View at Publisher · View at Google Scholar · View at MathSciNet
  19. X. T. Duong, J. Xiao, and L. Yan, “Old and new Morrey spaces with heat kernel bounds,” The Journal of Fourier Analysis and Applications, vol. 13, no. 1, pp. 87–111, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  20. H. Lin, E. Nakai, and D. Yang, “Boundedness of Lusin-area and gλ functions on localized Morrey-Campanato spaces over doubling metric measure spaces,” Journal of Function Spaces and Applications, vol. 9, no. 3, pp. 245–282, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  21. D. Yang, D. Yang, and Y. Zhou, “Localized Morrey-Campanato spaces on metric measure spaces and applications to Schrödinger operators,” Nagoya Mathematical Journal, vol. 198, pp. 77–119, 2010. View at MathSciNet
  22. 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 MathSciNet
  23. D. Fan, Y. Pan, and D. Yang, “A weighted norm inequality for rough singular integrals,” The Tohoku Mathematical Journal, vol. 51, no. 2, pp. 141–161, 1999. View at Publisher · View at Google Scholar · View at MathSciNet
  24. D. Fan, S. Lu, and D. Yang, “Boundedness of operators in Morrey spaces on homogeneous spaces and its applications,” Acta Mathematica Sinica, vol. 14, pp. 625–634, 1998. View at MathSciNet
  25. W. Yuan, W. Sickel, and D. Yang, Morrey and Campanato meet Besov, Lizorkin and Triebel, vol. 2005 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  26. R. R. Coifman and C. Fefferman, “Weighted norm inequalities for maximal functions and singular integrals,” Polska Akademia Nauk, vol. 51, pp. 241–250, 1974. View at MathSciNet
  27. P. Guan and E. Sawyer, “Regularity estimates for the oblique derivative problem,” Annals of Mathematics, vol. 137, no. 1, pp. 1–70, 1993. View at Publisher · View at Google Scholar · View at MathSciNet
  28. L. De Rosa and C. Segovia, “Dual spaces for one-sided weighted Hardy spaces,” Revista de la Unión Matemática Argentina, vol. 40, no. 3-4, pp. 49–71, 1997. View at MathSciNet
  29. M. S. Riveros and A. de la Torre, “On the best ranges for Ap+ and RHr+,” Czechoslovak Mathematical Journal, vol. 51, no. 2, pp. 285–301, 2001. View at Publisher · View at Google Scholar · View at MathSciNet
  30. X. W. Li and D. C. Yang, “Boundedness of some sublinear operators on Herz spaces,” Illinois Journal of Mathematics, vol. 40, no. 3, pp. 484–501, 1996. View at MathSciNet