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Journal of Function Spaces
Volume 2015, Article ID 490259, 9 pages
http://dx.doi.org/10.1155/2015/490259
Research Article

Weighted Weak Local Hardy Spaces Associated with Schrödinger Operators

Beijing International Studies University, Beijing 100024, China

Received 11 April 2015; Revised 30 June 2015; Accepted 13 July 2015

Academic Editor: Guozhen Lu

Copyright © 2015 Hua Zhu. 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. D. Goldberg, “A local version of real Hardy spaces,” Duke Mathematical Journal, vol. 46, no. 1, pp. 27–42, 1979. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. B. Huy Qui, “Weighted Hardy spaces,” Mathematische Nachrichten, vol. 103, pp. 45–62, 1981. View at Publisher · View at Google Scholar · View at MathSciNet
  3. T. Schott, “Pseudodifferential operators in function spaces with exponential weights,” Mathematische Nachrichten, vol. 200, pp. 119–149, 1999. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. E. M. Stein, Harmonic Analysis: Real Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton University Press, Princeton, NJ, USA, 1993. View at MathSciNet
  5. M. E. Taylor, Pseudodifferential Operators and Nonlinear PDE, vol. 100 of Progress in Mathematics, Birkhäuser, Boston, Mass, USA, 1991.
  6. H. Triebel, Theory of Function Spaces, Birkhäuser, Basel, Switzerland, 1983.
  7. 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
  8. V. S. Rychkov, “Littlewood-Paley theory and function spaces with Aploc weights,” Mathematische Nachrichten, vol. 224, no. 1, pp. 145–180, 2001. View at Publisher · View at Google Scholar
  9. J. Duoandikoetxea, Fourier Analysis, vol. 29 of Graduate Studies in Mathematics, American Mathematical Society, Providence, RI, USA, 2000.
  10. J. García-Cuerva and J. Rubio de Francia, Weighted Norm Inequalities and Related Topics, North-Holland, Amsterdam, The Netherlands, 1985. View at MathSciNet
  11. L. Grafakos, Classical and Modern Fourier Analysis, Pearson Education, Upper Saddle River, NJ, USA, 2004.
  12. L. Tang, “Weighted local Hardy spaces and their applications,” Illinois Journal of Mathematics, vol. 56, no. 2, pp. 453–495, 2012. View at Google Scholar · View at MathSciNet · View at Scopus
  13. H. Zhu and L. Tang, “Weighted local Hardy spaces associated to Schrödinger operators,” http://arxiv.org/abs/1403.7641.
  14. R. Fefferman and F. Soria, “The space weak H1,” Studia Mathematica, vol. 8, pp. 1–16, 1987. View at Google Scholar
  15. H. Liu, “The weak Hp spaces on homogeneous groups,” in Harmonic Analysis (Tianjin, 1988), vol. 1494 of Lecture Notes in Mathematics, pp. 113–118, Springer, 1991. View at Google Scholar
  16. L. Tang, “The weighted weak local Hardy spaces,” Rocky Mountain Journal of Mathematics, vol. 44, no. 1, pp. 297–315, 2014. View at Google Scholar
  17. B. Bongioanni, E. Harboure, and O. Salinas, “Classes of weights related to Schrödinger operators,” Journal of Mathematical Analysis and Applications, vol. 373, no. 2, pp. 563–579, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. L. Tang, “Weighted norm inequalities for Schrödinger type operators,” Forum Mathematicum, vol. 27, no. 4, pp. 2491–2532, 2015. View at Publisher · View at Google Scholar · View at MathSciNet
  19. L. Tang, “Extrapolation from Aρ,, vector-valued inequalities and applications in the Schrödinger settings,” Arkiv för Matematik, vol. 25, no. 1, pp. 175–202, 2014. View at Publisher · View at Google Scholar
  20. F. W. Gehring, “The Lp-integrability of the partial derivatives of a quasiconformal mapping,” Acta Mathematica, vol. 130, pp. 265–277, 1973. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. J. Dziubański, G. Garrigós, T. Martínez, J. L. Torrea, and J. Zienkiewicz, “BMO spaces related to Schrödinger operators with potentials satisfying a reverse Hölder inequality,” Mathematische Zeitschrift, vol. 249, no. 2, pp. 329–356, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  22. Z. W. Shen, “Lp estimates for Schrödinger operators with certain potentials,” Annales de l'Institut Fourier, vol. 45, no. 2, pp. 513–546, 1995. View at Publisher · View at Google Scholar · View at MathSciNet
  23. J. Dziubanski and J. Zienkiewicz, “Hardy space H1 associated to Schrödinger operator with potential satisfying reverse Hölder inequality,” Revista Matemática Iberoamericana, vol. 15, no. 2, pp. 279–296, 1999. View at Google Scholar
  24. 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 MathSciNet
  25. D. Yang and S. Yang, “Weighted local Orlicz Hardy spaces with applications to pseudo-differential operators,” Dissertationes Mathematicae, vol. 478, p. 78, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  26. D. Yang, D. Yang, and Y. Zhou, “Endpoint properties of localized Riesz transforms and fractional integrals associated to Schrödinger operators,” Potential Analysis, vol. 30, no. 3, pp. 271–300, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus