Abstract and Applied Analysis
Volume 2008 (2008), Article ID 196498, 12 pages
http://dx.doi.org/10.1155/2008/196498
Research Article
Compact Weighted Composition Operators and Multiplication Operators between Hardy Spaces
1Department of Mathematics, Faculty of Science Division II, Tokyo University of Science, 4-6-1 Higashicho, Hitachi, Ibaraki 317-0061, Japan
2Department of Mathematics, University of Science and Technology of China, Hefei 230026, China
Received 27 August 2007; Accepted 10 February 2008
Academic Editor: Stephen Clark
Copyright © 2008 Sei-Ichiro Ueki and Luo Luo. 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
- B. R. Choe, “The essential norms of composition operators,” Glasgow Mathematical Journal, vol. 34, no. 2, pp. 143–155, 1992. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- P. Gorkin and B. D. MacCluer, “Essential norms of composition operators,” Integral Equations and Operator Theory, vol. 48, no. 1, pp. 27–40, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- P. Poggi-Corradini, “The essential norm of composition operators revisited,” in Studies on Composition Operators, vol. 213 of Contemporary Mathematics, pp. 167–173, American Mathematical Society, Providence, RI, USA, 1998. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- J. H. Shapiro, “The essential norm of a composition operator,” Annals of Mathematics, vol. 125, no. 2, pp. 375–404, 1987. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- S. Li and S. Stević, “Weighted composition operators between and -Bloch space in the unit ball,” to appear in Taiwanese Journal of Mathematics. View at Zentralblatt MATH · View at MathSciNet
- S. Li and S. Stević, “Weighted composition operators from to the Bloch space on the polydisc,” Abstract and Applied Analysis, vol. 2007, Article ID 48478, 13 pages pages, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- G. Mirzakarimi and K. Seddighi, “Weighted composition operators on Bergman and Dirichlet spaces,” Georgian Mathematical Journal, vol. 4, no. 4, pp. 373–383, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- S. Ohno, “Weighted composition operators between and the Bloch space,” Taiwanese Journal of Mathematics, vol. 5, no. 3, pp. 555–563, 2001. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- S. Ohno, K. Stroethoff, and R. Zhao, “Weighted composition operators between Bloch-type spaces,” The Rocky Mountain Journal of Mathematics, vol. 33, no. 1, pp. 191–215, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- S. Ohno and R. Zhao, “Weighted composition operators on the Bloch space,” Bulletin of the Australian Mathematical Society, vol. 63, no. 2, pp. 177–185, 2001. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- M. D. Contreras and A. G. Hernández-Díaz, “Weighted composition operators on Hardy spaces,” Journal of Mathematical Analysis and Applications, vol. 263, no. 1, pp. 224–233, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- M. D. Contreras and A. G. Hernández-Díaz, “Weighted composition operators between different Hardy spaces,” Integral Equations and Operator Theory, vol. 46, no. 2, pp. 165–188, 2003. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- ̆Z. ̆Cŭcković and R. Zhao, “Weighted composition operators on the Bergman space,” Journal of the London Mathematical Society, vol. 70, no. 2, pp. 499–511, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- ̆Z. ̆Cŭcković and R. Zhao, “Weighted composition operators between different weighted Bergman spaces and different Hardy spaces,” Illinois Journal of Mathematics, vol. 51, no. 2, pp. 479–498, 2007. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- S. Ueki, “Weighted composition operators between weighted Bergman spaces in the unit ball of ,” Nihonkai Mathematical Journal, vol. 16, no. 1, pp. 31–48, 2005. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- L. Luo, “The essential norm of a composition operator on Hardy space of the unit ball,” Chinese Annals of Mathematics (Series A, Chinese), vol. 28A, no. 6, pp. 805–810, 2007, preprint. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- W. Rudin, Function Theory in the Unit Ball of ℂn, vol. 241 of Fundamental Principles of Mathematical Science, Springer, New York, NY, USA, 1980. View at Zentralblatt MATH · View at MathSciNet
- S. C. Power, “Hörmander's Carleson theorem for the ball,” Glasgow Mathematical Journal, vol. 26, no. 1, pp. 13–17, 1985. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- B. D. MacCluer, “Compact composition operators on ,” The Michigan Mathematical Journal, vol. 32, no. 2, pp. 237–248, 1985. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- K. H. Zhu, “Duality of Bloch spaces and norm convergence of Taylor series,” The Michigan Mathematical Journal, vol. 38, no. 1, pp. 89–101, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- C. C. Cowen and B. D. MacCluer, Composition Operators on Spaces of Analytic Functions, Studies in Advanced Mathematics, CRC Press, Boca Raton, Fla, USA, 1995. View at Zentralblatt MATH · View at MathSciNet