Table of Contents Author Guidelines Submit a Manuscript
Journal of Function Spaces and Applications
Volume 2012 (2012), Article ID 923874, 21 pages
http://dx.doi.org/10.1155/2012/923874
Research Article

BMO-Boundedness of Maximal Operators and g-Functions Associated with Laguerre Expansions

LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China

Received 29 February 2012; Revised 21 May 2012; Accepted 21 June 2012

Academic Editor: Aurelian Gheondea

Copyright © 2012 Li Cha and Heping Liu. 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. G. Szegö, Orthogonal Polynomials, American Mathematical Society, Providence, RI, USA, 4th edition, 1975.
  2. A. Nowak and K. Stempak, β€œRiesz transforms and conjugacy for Laguerre function expansions of Hermite type,” Journal of Functional Analysis, vol. 244, no. 2, pp. 399–443, 2007. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  3. L. Cha and H. P. Liu, “BMO spaces for Laguerre expansions”. Accepted in Taiwanese Journal of Mathematics.
  4. J. Dziubański, β€œHardy spaces for Laguerre expansions,” Constructive Approximation, vol. 27, no. 3, pp. 269–287, 2008. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  5. J. Dziubański, G. Garrigós, T. Martínez, J. L. Torrea, and J. Zienkiewicz, β€œBMO 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 Β· View at Google Scholar Β· View at Zentralblatt MATH
  6. D. C. Yang, D. Y. Yang, and Y. Zhou, β€œLocalized BMO and BLO spaces on RD-spaces and applications to Schrödinger operators,” Communications on Pure and Applied Analysis, vol. 9, no. 3, pp. 779–812, 2010. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  7. I. Abu-Falahah, P. R. Stinga, and J. L. Torrea, β€œSquare functions associated to Schrödinger operators,” Studia Mathematica, vol. 203, no. 2, pp. 171–194, 2011. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  8. J. Betancor, J. C. Fariña, L. Rodríguez-Mesa, A. Sanabria, and J. L. Torrea, β€œTransference between Laguerre and Hermite settings,” Journal of Functional Analysis, vol. 254, no. 3, pp. 826–850, 2008. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  9. J. J. Betancor, S. M. Molina, and L. Rodríguez-Mesa, β€œArea Littlewood-Paley functions associated with Hermite and Laguerre operators,” Potential Analysis, vol. 34, no. 4, pp. 345–369, 2011. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  10. S. Thangavelu, Lectures on Hermite and Laguerre Expansions, vol. 42 of Mathematical Notes, Princeton University Press, Princeton, NJ, USA, 1993.
  11. C. Bennett, R. A. DeVore, and R. Sharpley, β€œWeak-L and BMO,” Annals of Mathematics. Second Series, vol. 113, no. 3, pp. 601–611, 1981. View at Publisher Β· View at Google Scholar
  12. E. M. Stein, Harmonic Analysis: Real Variable Methods, Orthogonality, and Oscillatory Integrals, vol. 43 of Princeton Mathematical Series, Princeton University Press, Princeton, NJ, USA, 1993.