Abstract and Applied Analysis

Commuting Quasihomogeneous Toeplitz Operator and Hankel Operator on Weighted Bergman Space

Jun Yang

Full-text: Open access

Abstract

We characterize the commuting Toeplitz operator and Hankel operator with quasihomogeneous symbols. Also, we use it to show the necessary and sufficient conditions for commuting Toeplitz operator and Hankel operator with ordinary functions.

Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 408168, 8 pages.

Dates
First available in Project Euclid: 27 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393511986

Digital Object Identifier
doi:10.1155/2013/408168

Mathematical Reviews number (MathSciNet)
MR3089531

Zentralblatt MATH identifier
1321.47074

Citation

Yang, Jun. Commuting Quasihomogeneous Toeplitz Operator and Hankel Operator on Weighted Bergman Space. Abstr. Appl. Anal. 2013 (2013), Article ID 408168, 8 pages. doi:10.1155/2013/408168. https://projecteuclid.org/euclid.aaa/1393511986


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References

  • A. Brown and P. R. Halmos, “Algebraic properties of Toeplitz operators,” Journal für die Reine und Angewandte Mathematik, vol. 213, pp. 89–102, 1963/1964.
  • S. Axler and Ž. Čučković, “Commuting Toeplitz operators with harmonic symbols,” Integral Equations and Operator Theory, vol. 14, no. 1, pp. 1–12, 1991.
  • Ž. Čučković and N. V. Rao, “Mellin transform, monomial symbols, and commuting Toeplitz operators,” Journal of Functional Analysis, vol. 154, no. 1, pp. 195–214, 1998.
  • I. Louhichi and L. Zakariasy, “On Toeplitz operators with quasihomogeneous symbols,” Archiv der Mathematik, vol. 85, no. 3, pp. 248–257, 2005.
  • Y. F. Lu and B. Zhang, “Commuting Hankel and Toeplitz operators on the Bergman space,” Chinese Annals of Mathematics A, vol. 32, no. 5, pp. 519–530, 2011.
  • B. Zhang, Y. Shi, and Y. Lu, “Algebraic properties of Toeplitz operators on the polydisk,” Abstract and Applied Analysis, vol. 2011, Article ID 962313, 18 pages, 2011.
  • B. Zhang and Y. Lu, “Toeplitz operators with quasihomogeneous symbols on the Bergman space of the unit ball,” Journal of Function Spaces and Applications, vol. 2012, Article ID 414201, 16 pages, 2012.
  • X. Dong and Z. Zhou, “Commuting quasihomogeneous Toeplitz operators on the harmonic Bergman space,” Complex Analysis and Operator Theory, 2012.
  • B. R. Choe, H. Koo, and Y. J. Lee, “Commuting Toeplitz ope-rators on the polydisk,” Transactions of the American Mathematical Society, vol. 356, no. 5, pp. 1727–1749, 2004.
  • Y. J. Lee, “Commuting Toeplitz operators on the Hardy space of the polydisk,” Proceedings of the American Mathematical Society, vol. 138, no. 1, pp. 189–197, 2010.
  • J. Yang, L. Liu, and Y. Lu, “Algebraic properties of Toeplitz ope-rators on the pluriharmonic Bergman space,” Journal of Function Spaces and Applications, vol. 2013, Article ID 578436, 12 pages, 2013.
  • N. L. Vasilevski, “Bergman space structure, commutative algebras of Toeplitz operators, and hyperbolic geometry,” Integral Equations and Operator Theory, vol. 46, no. 2, pp. 235–251, 2003.
  • N. L. Vasilevski, Commutative Algebras of Toeplitz Operators on the Bergman Space, vol. 185 of Operator Theory: Advances and Applications, Birkhäuser, Basel, Switzerland, 2008.