Table of Contents Author Guidelines Submit a Manuscript
Journal of Function Spaces
Volume 2015, Article ID 362681, 6 pages
http://dx.doi.org/10.1155/2015/362681
Research Article

The Improvement on the Boundedness and Norm of a Class of Integral Operators on Space

Department of Mathematics, Huzhou University, Huzhou, Zhejiang 313000, China

Received 14 July 2014; Accepted 27 August 2014

Academic Editor: Janusz Matkowski

Copyright © 2015 Lifang Zhou and Jin Lu. 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. O. Kures and K. Zhu, “A class of integral operators on the unit ball of Cn,” Integral Equations and Operator Theory, vol. 56, no. 1, pp. 71–82, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. K. Zhu, “A sharp norm estimate of the Bergman projection in Lp spaces,” in Bergman Spaces and Related Topics in Complex Analysis, vol. 404 of Contemporary Mathematics, pp. 195–205, American Mathematical Society, Providence, RI, USA, 2006. View at Google Scholar
  3. K. Zhu, Operator Theory in Function Spaces, American Mathematical Society, Providence, RI, USA, 2nd edition, 2007.
  4. K. Zhu, Spaces of Holomorphic Functions in the Unit Ball, Springer, New York, NY, USA, 2005. View at MathSciNet
  5. P. Ahern, M. Flores, and W. Rudin, “An invariant volume-mean-value property,” Journal of Functional Analysis, vol. 111, no. 2, pp. 380–397, 1993. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. F. A. Berezin, “Covariant and contravariant symbols of operators,” Mathematics of the USSR-Izvestiya, vol. 6, no. 5, pp. 1117–1151, 1972. View at Publisher · View at Google Scholar
  7. H. Hedenmalm, B. Korenblum, and K. Zhu, Theory of Bergman spaces, Springer, New York, NY, USA, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  8. M. Dostanić, “Norm of Berezin transform on LP space,” Journal d'Analyse Math\'ematique, vol. 104, pp. 13–23, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  9. C. Liu and L. Zhou, “On the p-norm of the Berezin transform,” Illinois Journal of Mathematics, vol. 56, no. 2, pp. 497–505, 2012. View at Google Scholar · View at MathSciNet
  10. D. Li and C. Liu, “The mean-value property and (α,β)-harmonicity,” Journal of the Australian Mathematical Society, vol. 91, no. 2, pp. 189–206, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  11. A. Erdélyi, W. Magnus, F. Oberhettinger, and F. Tricomi, Higher Transcendental Functions, vol. 1, McGraw-Hill, New York, NY, USA, 1953.
  12. C. Liu, “Sharp Forelli-Rudin esitimates and the norm of the Bergman projection,” Preprint.
  13. W. Rudin, Function Theory in the Unit Ball of n, Springer, New York, NY, USA, 2008. View at MathSciNet